John Etnyre
Introduction to Algebraic Topology
These notes give an introduction to Algebraic Topology without assuming any familiarity with topology or algebra! There is also an emphasis on knot theory as a running theam.
Introduction to Algebraic Topology
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Knot Theory
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Knots and Links
Knot Coloring
Alexander Polynomial
Jones Polynomial
Alternating Links
Other Polynomials
Introduction to Topology
Topological Spaces
Sequences and Limit Points
Continuous Functions
Connectedness
Compactness
Quotient Spaces
Manifolds
Definitions and First Examples
1-manifolds
2-manifolds
Groups
Basic Group Theory
Group Presentations
Braid Groups and the Jones Polynomial
The Fundamental Group
Definition of the Fundamental Group
undamental Group of S^1
Applications
Seifert-Van Kampen Theorem
Free Products with Amalgamations
Seifert-Van Kampen Theorem
Fundamental Groups, Surfaces, and the 1st Homology
Groups and Topology
Knot Groups and Colorings
Knot Groups
Coloring Knots
Covering Spaces
Covering Spaces
Subgroups
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