Spring 2020

Hatcher section 1.A

Munkres chapter 14

Office hours will be M 11-12, T 3:30-4:30 and F 1:30-2:30.

The primary textbook for this class will be

Algebraic Topology by Hatcher and

Due | Assignment | Reading (Pages from Lee) |
---|---|---|

1/22 | Ex 7.6, a careful homotopy for Th. 7.11c, P. 7-1, 7-3, 7-10 | 183-195, 197-199 |

1/29 | 7-4, 7-5, 7-2, 7-6 | 199-205, 205-208, 217-220 |

2/5 | 7-9, 7-11, 7-19, 8-1 (you can use the fact that the fundamental group of the circle is non trivial.), 8-7 | 220-224, 225-229 |

2/12 | 8-4, 8-11, 8-6, 8-8 | 277-283 |

2/19 | 11-2, 11-4, 11-12, 11-13, 11-14 | 283-287, 287-291 |

2/26 | 12-2c, 12-3 | 292-297 |

3/4 | 11-16, 11-20, 11-17 (you can replace the space by the wedge of S1 and S2 if you want), 11-18 | 297-302 |

3/11 | 11-19, 12-4, 12-15 (you can use Theorem 12.18, 6.16, 6.17), 12-12 | 307-311, 311-322, 233-244 |

3/25 | 9-1, 9-4, 10-1, 10-2, 10-5, 10-9 | 251-257, 261-264, 264-273 |

4/1 | 9-5, 10-6, 10-21, 10-7, 10-13 | |

4/8 | 10-3, 10-20, 10-19, Compute some homology | 339-347 |

4/15 | Compute the simplicial homology of the Klein bottle and sphere, Practice with exactness | 347-355 |

4/22 | 13-2, 13-6, 13-3, 13-7, Show that the quotient map S^1\times S^1\to S^2 collapsing the subspace S^1 \vee S^1 to a point is not nullhomotopic by showing that it induces an isomorphism on H_2. On the other hand, show via covering spaces that any map S^2 \to S^1\times S^1 is nullhomotopic. (You can use the fact that X\cup C(A) is homotopy equivalent to X/A if X and A are CW complexes.) | 355-363 |

4/29 | Homology of spaces Now three problems! |
363-366, 369-374 |