Course description
This is a graduate course in algebraic topology covering homology.
Course instructor: Laura Starkston
- Email: lstarkston AT ucdavis.edu
- Office hour: Monday 3-4pm Pacific
Texts
We will primarily follow Hatcher's Algebraic Topology Chapter 2.
Another reference for the course is Homotopical Topology by Fomenko and Fuchs, Lectures 12-15.
Topics
- Simplicial and singular homology
- Induced maps and invariance
- Exact sequence of a pair
- Excision
- Homology of Spheres, Degree of a map
- Cellular homology
- Mayer-Vietoris
- Axiomatic definition
- Homology with coefficients
- Hurewicz theorem
- Possibly Lefschetz fixed point theorem and/or Kunneth formula