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2:30-2:35 |
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Welcome |
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2:35-2:55 |
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Tea |
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2:55-3:00 |
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Welcome, Part II |
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3:00-3:50 |
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Colloquium: Bena Tshishiku |
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Nielsen realization problems
Slides |
4:00-5:00 |
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Lightning talk session 1 |
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8 talks see below
Slides |
5:30- |
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Virtual Pictionary and Zoom Hangout/Happy hour |
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10:00-10:10 |
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Tea |
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10:10-10:15 |
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Conference Photo |
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10:15-10:45 |
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Arunima Ray |
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Embedding surfaces in 4-manifolds
Slides |
10:50-11:20 |
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Miriam Kuzbary
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Pure Braids and Link Concordance
Slides |
11:25-11:35 |
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Break from computer |
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11:35-12:30 |
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Lighting talk session 2 |
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7 talks see below
Slides |
12:30-1:15 |
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Lunch Break |
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1:15-1:45 |
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Nathan Broaddus
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The mapping class group of the connect sums of S^2xS^1
Slides |
1:45-2:00 |
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Tea Break |
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2:00-2:30 |
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Michelle Chu
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Prescribed virtual torsion in the homology of 3-manifolds
Slides |
4:00- |
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Virtual Codenames and Zoom Hangout/Happy Hour |
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10:00-10:15 |
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Tea |
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10:15-10:45 |
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Andras Stipsicz
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The purely cosmetic surgery conjecture for pretzel knots
Slides |
10:50-11:20 |
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Akram Alishahi
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A Contact invariant from Heegaard Floer homology
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11:25-12:25 |
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Lighting talk session 3 |
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8 talks see below
Slides |
12:25-1:00 |
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Last conference tea |
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| | Emily Shinkle | Finite Rigid Sets in Flip Graphs |
| | Agniva Roy | Symplectic fillings of lens spaces. |
| | Aaron Calderon | Vector fields, mapping class groups, and holomorphic 1-forms |
| | Lily Li | Bounding Link Volumes via Subdivision |
| | Josh Pankau | Pseudo-Anosov Stretch Factors and Coxeter Transformations |
| | Orsola Capovilla-Searle | Weinstein handle decompositions of complements of toric divisors in toric 4 manifolds |
| | Robert DeYeso | Integral Klein bottle surgeries and Heegaard Floer homology |
| | Rylee Lyman | Nielsen Realization for Infinite-Type Surfaces |
| | Sarah Blackwell | 2-Knot Group Trisections |
| | Noah Caplinger | Small Quotients of Braid Groups |
| | Fraser Binns | Link Detection Results for Knot Floer Homology |
| | Marissa Miller | Mapping class groups vs. handlebody groups |
| | Ceren Kose | Symmetric unions and reducible fillings |
| | Anubhav Mukherjee | On embeddings of 3-manifolds in symplectic 4-manifolds |
| | Benjamin Ruppik | Deep and shallow slice knots in 4-manifolds |
| | Marius Huber | Ribbon cobordisms between lens spaces |
| | Puttipong Pongtanapaisan | Bridge surfaces with non-contractible disk complex |
| | Ipsita Datta | Obstructions to the existence of Lagrangians in $\R^4$ |
| | Hugo Zhou | Homology concordance and an infinite rank subgroup |
| | Qing Liu | Rigidity on the Morse boundary |
| | Hannah Turner | Visibility of symmetries, L-spaces, and branched cyclic covers |
| | Melissa Zhang | Upsilon-like Concordance Invariants from Khovanov Homology |
| | Hyun Ki Min | Exotic 4-manifolds with boundary |
Titles and Abstracts
A Contact invariant from Heegaard Floer homology
Several effective and powerful invariants have been defined using Heegaard Floer homology over the past two decades. We will describe a new addition to this collection which behaves nicely under gluing. This invariant is defined for a contact 3-manifold with a foliated boundary and lives in the bordered sutured Floer homology. This is joint work with Foldvari, Hendricks, Licata, Petkova, and Vertesi.
The mapping class group of the connect sums of S^2xS^1
Let M_n be the connect sum of n copies of S^2xS^1. By a theorem of Laudenbach, the mapping class group, Mod(M_n), of M_n is an extension of the outer automorphism group Out(F_n) of the free group F_n by the finite abelian subgroup Twist(M_n) generated by Dehn twists about embedded 2-spheres. We give a new proof of Laudenbach’s result utilizing the set of trivializations of the tangent bundle TM_n and further show that the extension Twist(M_n) -> Mod(M_n) -> Out(F_n) splits.
Prescribed virtual torsion in the homology of 3-manifolds
Hongbin Sun showed that a closed hyperbolic 3-manifold virtually contains any prescribed torsion subgroup as a direct factor in homology. In this talk we will discuss joint work with Daniel Groves generalizing Sun’s result to irreducible 3-manifolds which are not graph-manifolds.
Pure Braids and Link Concordance
The knot concordance group can be contextualized as organizing problems about 3- and 4-dimensional spaces and the relationships between them. Every 3-manifold is surgery on some link, not necessarily a knot, and thus it is natural to ask about such a group for links. In 1988, Le Dimet constructed the string link concordance groups and in 1998, Habegger and Lin precisely characterized these groups as quotients of the link concordance sets using a group action. Notably, the knot concordance group is abelian while, for each n, the string link concordance group on n strands is non-abelian as it contains the pure braid group on n strands as a subgroup. In this talk, I will discuss my result the quotient of each string link concordance group by its pure braid subgroup is non-abelian.
Embedding surfaces in 4-manifolds
When is a given map of a surface to a 4-manifold homotopic to an embedding? I’ll motivate this question and give a (short) survey of related results, including the work of Freedman and Quinn, and culminating in a general surface embedding theorem. The talk will be based on joint work with Daniel Kasprowski, Mark Powell, and Peter Teichner.
The purely cosmetic surgery conjecture for pretzel knots
According to the purely cosmetic surgery conjecture, the oriented diffeomorphism type of the result of a Dehn surgery along a fixed nontrivial knot determines the surgery slope. As an application of the theorem of Hanselman we show that pretzel knots satisfy this conjecture. Along the way we show a simple way to estimate the thickness of a knot. This is joint work with Zoltan Szabo.
Nielsen realization problems
For a manifold M, the (generalized) Nielsen realization problem asks if the surjection Diff(M) → π_0 Diff(M) is split, where Diff(M) is the diffeomorphism group. When M is a surface, this question was posed by Thurston in Kirby's problem list and was addressed by Morita. I will discuss some more recent work on Nielsen realization problems with connections to flat fiber bundles, K3 surfaces, and smooth structures on hyperbolic manifolds.
Lightning talk
Link Detection Results for Knot Floer Homology
Given a link invariant, one can ask "how good is this link invariant at distinguishing links"? In this talk I will discuss recent work showing that Knot Floer homology is very good at distinguishing various simple links from all others. This is joint work with Gage Martin.
2-Knot Group Trisections
A trisection of a 4-manifold induces a Van Kampen cube of fundamental groups coming from the pieces of the trisection, and more surprisingly, vice versa. That is, a Van Kampen cube satisfying a few simple requirements produces a trisection of a 4-manifold. One natural question to ask is whether the same holds for bridge trisections of knotted surfaces in S^4. In this talk I will introduce this question along with relevant definitions, and briefly describe progress towards a resolution. This is joint work with Rob Kirby, Michael Klug, Vince Longo, and Ben Ruppik.
Vector fields, mapping class groups, and holomorphic 1-forms
Given a vector field on a surface, which homeomorphisms preserve (the isotopy class of) this vector field? Despite the fundamental nature of this question, little is known about these “framed mapping class groups.” In this talk I will describe some recent joint work with Nick Salter in which we give explicit, finite generating sets for framed mapping class groups, as well as highlight an application to the topology of moduli spaces of holomorphic 1-forms.
Small Quotients of Braid Groups
We prove that the symmetric group S_n is the smallest non-cyclic quotient of the braid group B_n.
Weinstein handle decompositions of complements of toric divisors in toric 4 manifolds
We consider toric 4 manifolds with certain toric divisors that have normal crossing singularities. The normal crossing singularities can be smoothed, changing the topology of the complement. In specific cases this complement has a Weinstein structure, and we develop an algorithm to construct a Weinstein handlebody diagram of the complement of the smoothed toric divisor. The algorithm we construct more generally gives a Weinstein handlebody diagram for Weinstein 4-manifolds constructed by attaching 2 handles to T*S for any surface S, where the 2 handles are attached along the conormal lift of curves on S. Joint work with Bahar Acu, Agnes Gadbled, Aleksandra Marinkovic, Emmy Murphy, Laura Starkston and Angela Wu.
Obstructions to the existence of Lagrangians in $\R^4$
We present some obstructions to the existence of exact Lagrangian surfaces which are cobordisms in $\R^4$ between links lying in parallel copies of $\R^3$. The obstructions arise from considering moduli spaces of holomorphic disks with boundary on related Lagrangian cobordisms between immersed links. We present examples of pairs of knots that cannot be Lagrangian cobordant and knots which cannot bound Lagrangian surfaces.
Integral Klein bottle surgeries and Heegaard Floer homology
In low-dimensional topology we are often interested in determining 3-manifolds that arise as surgery along a knot, and investigating the surfaces they contain. In this talk, we study gluings X of the twisted I-bundle over the Klein bottle to knot complements, and investigate which gluings can be realized as integral Dehn surgery along a knot in S^3. All closed, orientable 3-manifolds containing a Klein bottle can be presented as such a gluing, and Heegaard Floer homology provides a way to study surgery obstructions. Using recent immersed curves techniques, we prove that if X is 8-surgery along a genus two knot and arises as such a gluing with an S^3 knot complement, then it is an L-space and the surgery knot has the same knot Floer homology as the (2,5)-torus knot.
Ribbon cobordisms between lens spaces
The question of when there exists a rational homology cobordism between two lens spaces was completely answered by Lisca. A refinement of this question is to ask when there exists a ribbon rational homology cobordism from one lens space to another, i.e. one that can be built using just 1- and 2-handles. In this talk, I will illustrate that Lisca's machinery can be used to answer this question.
Symmetric unions and reducible fillings
Symmetric unions are a class of ribbon knots that admit particularly nice diagrams. Like the slice-ribbon conjecture, one may ask whether every ribbon knot is a symmetric union. This too in general has turned out to be a challenging problem; however, there is some mileage in obstructing a knot to admit certain symmetric union diagrams. In my talk I will describe a way to make use of this symmetry in studying their double branched covers to obtain such an obstruction.
Bounding Link Volumes via Subdivision
Given a link in a 3-manifold that can be appropriately decomposed into tangles, we attempt to bound the volume of the link by studying its constituent tangles. In particular, we associate to the constituent pieces a notion of hyperbolicity and volume. Using results of Agol-Storm-Thurston, we obtain surprisingly accurate lower bounds on the volumes of the links from the sum of the volumes of the constituent tangles in various 3-manifolds.
Rigidity on the Morse boundary
The Morse boundary of a proper geodesic metric space is a quasi-isometry invariant to study hyperbolic-like behaviors in the space. A quasi-isometry between two spaces induces a homeomorphism on their Morse boundaries. This homeomorphism satisfies a variety of metric properties including bi-hölder, quasi-conformal, quasi-möbius and power quasisymmetric. In this talk, we will investigate these structures on the Morse boundary which determine the interior space up to a quasi-isometry.
Nielsen Realization for Infinite-Type Surfaces
A famous theorem of Kerckhoff from 1983 solved the Nielsen realization problem in the affirmative: finite subgroups of mapping class groups arise as groups of isometries of hyperbolic metrics on the surface. We extend this theorem to the infinite-type setting and discuss some group-theoretic consequences.
Mapping class groups vs. handlebody groups
In this talk, I will discuss handlebody groups and their relationship to mapping class groups. I will discuss the similar definitions of these groups, and their related simplicial graphs. I will also discuss some key differences that have been proven regarding their geometries, including their statuses as hierarchically hyperbolic groups and the characterizations of their stable subgroups.
Exotic 4-manifolds with boundary
One of important projects in low-dimensional topology is to figure out which 4-manifolds admit exotic smooth structures. In this talk, we consider the relative version of this question: given a 3-manifold, does it bound a compact 4-manifold which admits infinitely many smooth structures? We give several criteria when a 3-manifold bounds an exotic 4-manifold. This is a joint work with John Etnyre and Anubhav Mukherjee.
On embeddings of 3-manifolds in symplectic 4-manifolds
In this talk I will discuss the conjecture that every 3 manifolds can be smoothly embedded in symplectic 4 manifolds. I will give some motivation on why is this an interesting conjecture. And state a few results.
Pseudo-Anosov Stretch Factors and Coxeter Transformations
Associated to every pseudo-Anosov mapping class is a bi-Perron unit called the stretch factor. It was conjectured by Fried that every bi-Perron unit has a power that is a stretch factor. In this lightning talk, I will discuss some results towards resolving Fried's conjecture as well as a connection between stretch factors and spectral radii of bipartite Coxeter transformations.
Bridge surfaces with non-contractible disk complex
A crucial step in the proofs of various theorems about 3-manifolds involves isotoping two surfaces to intersect nicely. This can certainly be done if the two surfaces are incompressible. However, Bachman showed that the incompressibility assumption could be relaxed if the disk complex of one of the surfaces is not contractible. Thus, it is interesting to study the homotopy groups of the disk complex. In this talk, I will give examples of bridge surfaces whose disk complex is simply connected, but not 2-connected.
Symplectic fillings of lens spaces.
I will discuss recent work where the classification (upto diffeomorphism) of symplectic fillings of lens spaces was completed. The talk will also explore two research directions stemming from the result, relating to symplectic cobordisms between lens spaces and contact lens space realisation, and share some interesting open questions. This is joint work with John Etnyre. The classification result was also obtained independently by Austin Christian and Youlin Li.
Deep and shallow slice knots in 4-manifolds
This is an advertisement for joint work with Michael Klug. We define deep slice knots in the boundary of a 4-manifold: Such knots bound a slice disk in the manifold but none that lives in a collar neighborhood of the boundary, i.e. to slice such a knot you have to go deep into the 4-manifold. Every 4-manifold built from a 0-handle and a non-zero number of 2-handles has a deep slice knot in its boundary.
Finite Rigid Sets in Flip Graphs
The mapping class group of a surface gives us a sense of the "symmetries" of the surface. One way of studying this group is via its action on a metric space, such as the flip graph. Korkmaz-Papadopoulus and Aramayona-Koberda-Parlier have shown a one-to-one correspondence between elements of the mapping class group and the automorphisms they induce on the flip graph. I've shown that flip graphs also have "finite rigid subgraphs," which gives us a third set in this one-to-one correspondence, and unlike the previous two sets, the elements in this third set are maps with a fixed finite domain.
Visibility of symmetries, L-spaces, and branched cyclic covers
Recently, Costa and Van Quach Hongler showed that a prime alternating knot with a (periodic) symmetry must show this symmetry in an alternating diagram if the order of the symmetry is at least 3. This result can be applied to obstruct symmetries and to study uniqueness questions for branched cyclic covers. In this talk, I'll discuss a result which shows the degree to which the Costa-Van Quach Hongler result fails if the order of the symmetry is allowed to be 2.
Upsilon-like Concordance Invariants from Khovanov Homology
Upsilon-like invariants from knot Floer homology have helped us study the knot concordance group. I will discuss work-in-progress with Ross Akhmechet on an Upsilon-like concordance invariant from Khovanov homology.
Homology concordance and an infinite rank subgroup
Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group CZ_hat (resp. CZ) was previously defined as the set of knots in homology spheres that bounds homology balls (resp. in three sphere), modulo homology concordance. We prove CZ_hat quotient by CZ contains an infinite rank subgroup. We construct our family of examples by applying the filtered mapping cone formula to L-space knots, and prove linear independence with the help of the connected knot complex
