Math 205B, Algebraic Topology

Winter 2013

MWF 10:10-11 am, Surge 284

Course Information

Monday, January 7: Equivalence of covering spaces and the lifting criterion

Wednesday, January 9: Classifying covering spaces

          Homework: Munkres 79 #1, 2 (due Monday, January 14)

Friday, January 11: Universal covering spaces

Monday, January 14: Covering transformations

          Homework: Munkres 79 #3, 4 (due Wednesday, January 23)

Wednesday, January 16: Regular covering spaces

Friday, January 18: Regular covering spaces as quotients

          Homework: Munkres 81 #2, 3 (due Wednesday, January 23)

Monday, January 21: No class

Wednesday, January 23: Existence of covering spaces and more examples

          Homework can be found under Assignments on iLearn

Friday, January 25: CW complexes

Monday, January 28: Euler characteristic

          Homework 3 due

Wednesday, January 30: Intro to homology

Friday, February 1: Simplicial/polyhedral homology computations

Monday, February 4: Definition of singular homology

          Homework 4 due

Wednesday, February 6: Singular homology as a functor

Friday, February 8: Homotopy invariance

Monday, February 11: Long exact sequence of a pair

          Homework 5 due

Wednesday, February 13: Midterm exam

Friday, February 15: Excision and the homology of spheres

Monday, February 18: No class

Wednesday, February 20: Barycentric subdivision

          Homework 6 due

Friday, February 22: Barycentric subdivision, continued

Monday, February 25: Completion of proof of excision and some applications

          Homework 7 due

Wednesday, February 27: Homology of quotient spaces

Friday, March 1: Cellular homology

Monday, March 4: Equivalence of singular and cellular homology

          Homework 8 due

Wednesday, March 6: Degree

Friday, March 8: Local degree and homology calculations

Monday, March 11: Mayer-Vietoris sequence

          Homework 9 due

Wednesday, March 13: Examples using Mayer-Vietoris

Friday, March 15: Euler characteristic revisited

          Recommended problems for practice: Hatcher 2.2 #22, 28, 34

Office hours for finals week: Monday and Tuesday 2-3 (can drop by at other times also)

Wednesday, March 20: Final exam 8-11 am

Last updated: 15 March 2013