MATH 537 Algebraic Topology Fall 2019
webpage:http://metu.edu.tr/~beyaz/537/ Last updated January 4, 2020
Schedule:
1-Homotopy and homotopy equivalence
2-Quotient topology, CW complexes
3-Homotopy extension property
4-Fundamental group, simply connectedness
5-Fundamental group of the circle
6-Induced homomorphisms
7-Van Kampen's theorem, applications
8-Covering spaces, Homotopy lifting property
9-Classification of covering spaces
10-Deck transformations and group actions
11-Delta complexes and simplicial homology
12-Singular homology, homological algebra
13-Homotopy invariance, relative homology groups
14-Excision, cellular homology, Mayer-Vietoris sequence
Sources:
A. Hatcher, Algebraic Topology, 2001
J.R. Munkres, Topology, 2000
Catalog Description:
Fundamental group, Van Kampen’s Theorem, covering spaces. Singular
homology: Homotopy invariance, homology long exact sequence,
Mayer-Vietoris sequence, excision. Cellular homology. Homology with
coefficients. Simplicial homology and the equivalence of simplicial and
singular homology. Axioms of homology. Homology and fundamental groups.
Simplicial approximation. Applications of homology.
Lecture Time and Place:
Tuesday 13:40-14:30 M231
Wednesday 13:40-15:30 M231