home

This is the webpage for my fall 2021 section of Math 151a (algebraic and differential topology).

The syllabus is posted here. This is subject to minor revisions, as necessary. In the interest of transparency, all versions will remain available at this webpage.
version replaced 10/10 available here (changed office hours)

schedule:
week topics readings homework due date
1 (9/27-10/1) overview (homology, cohomology, Poincaré duality); Δ-complexes and simplicial homology §2.1 hw1 10/6
2 (10/4-10/8) singular homology: first deductions, homotopy invariance, long exact sequence §2.1 hw2 10/13
3 (10/11-10/15) proof of long exact sequence: relative homology, five lemma, excision §2.1 hw3 10/20
4 (10/18-10/22) the derived perspective, equivalence of simplicial and singular homology, CW-complexes §2.1, §0 hw4 10/27
5 (10/25-10/29) CW-structure of CPn, degree, vector fields on spheres §0, §2.2 hw5 11/3
6 (11/1-11/5) cellular homology, Euler characteristic §2.2 hw6 11/10
7 (11/8-11/12) Mayer--Vietoris, homology with coefficients, introduction to cohomology §2.2, §3.1 hw7 11/17
8 (11/15-11/19) universal coefficient theorem, cohomology of spaces §3.1 hw8 11/24
9 (11/22-11/26) cup product §3.2 hw9 12/1
10 (11/29-12/3) Poincaré duality §3.3 hw10 12/8