Georgia Institute of Technology
December 4 to 6, 2020

 
 
 
             

Schedule

Friday        
2:30-2:35
  Welcome    
2:35-2:55
  Tea    
2:55-3:00
  Welcome, Part II    
3:00-3:50
  Colloquium: Bena Tshishiku   Nielsen realization problems
Slides
4:00-5:00
  Lightning talk session 1   8 talks see below
Slides
5:30-
  Virtual Pictionary and Zoom Hangout/Happy hour  
Saturday        
10:00-10:10
  Tea    
10:10-10:15
  Conference Photo    
10:15-10:45
  Arunima Ray   Embedding surfaces in 4-manifolds
Slides
10:50-11:20
  Miriam Kuzbary   Pure Braids and Link Concordance
Slides
11:25-11:35
  Break from computer  
11:35-12:30
  Lighting talk session 2   7 talks see below
Slides
12:30-1:15
  Lunch Break  
1:15-1:45
  Nathan Broaddus   The mapping class group of the connect sums of S^2xS^1
Slides
1:45-2:00
  Tea Break    
2:00-2:30
  Michelle Chu   Prescribed virtual torsion in the homology of 3-manifolds
Slides
4:00-
  Virtual Codenames and Zoom Hangout/Happy Hour  
Sunday        
10:00-10:15
  Tea    
10:15-10:45
  Andras Stipsicz   The purely cosmetic surgery conjecture for pretzel knots
Slides
10:50-11:20
  Akram Alishahi   A Contact invariant from Heegaard Floer homology
Slides
11:25-12:25
  Lighting talk session 3   8 talks see below
Slides
12:25-1:00
  Last conference tea  

 


Lightning talks session 1:

  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

Lightning talks session 2:

  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

Lightning talks session 3:

  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

Akram Alishahi
Title: A Contact invariant from Heegaard Floer homology
Abstract: 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.

Nathan Broaddus
Title: The mapping class group of the connect sums of S^2xS^1
Abstract: 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.

Michelle Chu
Title: Prescribed virtual torsion in the homology of 3-manifolds
Abstract: 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.

Miriam Kuzbary
Title: Pure Braids and Link Concordance
Abstract: 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.

Arunima Ray
Title: Embedding surfaces in 4-manifolds
Abstract: 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.

Andras Stipsicz
Title: The purely cosmetic surgery conjecture for pretzel knots
Abstract: 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.

Bena Tshishiku
Title: Nielsen realization problems
Abstract: 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

Fraser Binns
Title: Link Detection Results for Knot Floer Homology
Abstract: 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.

Sarah Blackwell
Title: 2-Knot Group Trisections
Abstract: 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.

Aaron Calderon
Title: Vector fields, mapping class groups, and holomorphic 1-forms
Abstract: 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.

Noah Caplinger
Title: Small Quotients of Braid Groups
Abstract: We prove that the symmetric group S_n is the smallest non-cyclic quotient of the braid group B_n.

Orsola Capovilla-Searle
Title: Weinstein handle decompositions of complements of toric divisors in toric 4 manifolds
Abstract: 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.

Ipsita Datta
Title: Obstructions to the existence of Lagrangians in $\R^4$
Abstract: 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.

Robert DeYeso
Title: Integral Klein bottle surgeries and Heegaard Floer homology
Abstract: 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.

Marius Huber
Title: Ribbon cobordisms between lens spaces
Abstract: 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.

Ceren Kose
Title: Symmetric unions and reducible fillings
Abstract: 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.

Lily Li
Title: Bounding Link Volumes via Subdivision
Abstract: 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.

Qing Liu
Title: Rigidity on the Morse boundary
Abstract: 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.

Rylee Lyman
Title: Nielsen Realization for Infinite-Type Surfaces
Abstract: 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.

Marissa Miller
Title: Mapping class groups vs. handlebody groups
Abstract: 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.

Hyun Ki Min
Title: Exotic 4-manifolds with boundary
Abstract: 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.

Anubhav Mukherjee
Title: On embeddings of 3-manifolds in symplectic 4-manifolds
Abstract: 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.

Josh Pankau
Title: Pseudo-Anosov Stretch Factors and Coxeter Transformations
Abstract: 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.

Puttipong Pongtanapaisan
Title: Bridge surfaces with non-contractible disk complex
Abstract: 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.

Agniva Roy
Title: Symplectic fillings of lens spaces.
Abstract: 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.

Benjamin Ruppik
Title: Deep and shallow slice knots in 4-manifolds
Abstract: 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.

Emily Shinkle
Title: Finite Rigid Sets in Flip Graphs
Abstract: 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.

Hannah Turner
Title: Visibility of symmetries, L-spaces, and branched cyclic covers
Abstract: 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.

Melissa Zhang
Title: Upsilon-like Concordance Invariants from Khovanov Homology
Abstract: 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.

Hugo Zhou
Title: Homology concordance and an infinite rank subgroup
Abstract: 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

organizers: W. Bloomquist, J. Etnyre, J. Hom, S. Krishna, M. Kuzbary, B. Liu, D. Margalit, and J. Park
Supported by the NSF and the Georgia Institute of Technology