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.
  1. Introduction to Algebraic Topology.
  2. Knot Theory.
    1. Knots and Links
    2. Knot Coloring
    3. Alexander Polynomial
    4. Jones Polynomial
    5. Alternating Links
    6. Other Polynomials
  3. Introduction to Topology
    1. Topological Spaces
    2. Sequences and Limit Points
    3. Continuous Functions
    4. Connectedness
    5. Compactness
    6. Quotient Spaces
  4. Manifolds
    1. Definitions and First Examples
    2. 1-manifolds
    3. 2-manifolds
  5. Groups
    1. Basic Group Theory
    2. Group Presentations
    3. Braid Groups and the Jones Polynomial
  6. The Fundamental Group
    1. Definition of the Fundamental Group
    2. undamental Group of S^1
    3. Applications
  7. Seifert-Van Kampen Theorem
    1. Free Products with Amalgamations
    2. Seifert-Van Kampen Theorem
    3. Fundamental Groups, Surfaces, and the 1st Homology
    4. Groups and Topology
  8. Knot Groups and Colorings
    1. Knot Groups
    2. Coloring Knots
  9. Covering Spaces
    1. Covering Spaces
    2. Subgroups