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 CP^{n}, 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 |