Math 6801

Algebraic Topology 1

Fall 2017

Lecturer: Michael Davis

Office: MW (Math Tower) 616

E-mail: davis.12@osu.edu

Phone: 292-4886

Office hours: MWF 10:10 - 11:00 AM or by appointment

Text: Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002. ISBN 0-521-79540-0

http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Class: MWF 9:10 - 10:05 AM, University Hall 086, Call no. 16815

Catalog Description: Simplicial and CW- complexes, operations on spaces; homotopy and homeomorphism type; fundamental group,

Seifert Van-Kampen Theorem; classification of covering spaces; singular and simplicial homology, chain maps, homotopy invariance, functoriality.

In the fall semester we will concentrate on the fundamental group and the theory of covering spaces.

Then we will begin homology theory.

My homepage: click here Math Department's webpage: click here

**Lecture notes:** Aug
22-28, Aug
30-Sept 1, Sept
6-11, Sept
12-20, Sept
21-29, Oct..
1-10, Oct.18,
Oct.
22-Nov. 3, Nov.
5-14,

Nov.19-28,

**Midterm: **in
class, Friday, October 20 (on fundamental group and covering
spaces)

**Last homework:** will be
graded and = final. due Dec. 6

**Trees
**(Serre's book), Carlsson's
paper

Algebraic Topology 1

Fall 2017

Lecturer: Michael Davis

Office: MW (Math Tower) 616

E-mail: davis.12@osu.edu

Phone: 292-4886

Office hours: MWF 10:10 - 11:00 AM or by appointment

Text: Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002. ISBN 0-521-79540-0

http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Class: MWF 9:10 - 10:05 AM, University Hall 086, Call no. 16815

Catalog Description: Simplicial and CW- complexes, operations on spaces; homotopy and homeomorphism type; fundamental group,

Seifert Van-Kampen Theorem; classification of covering spaces; singular and simplicial homology, chain maps, homotopy invariance, functoriality.

In the fall semester we will concentrate on the fundamental group and the theory of covering spaces.

Then we will begin homology theory.

My homepage: click here Math Department's webpage: click here

Nov.19-28,

Homework Assignments

Number |
Due Date |
pages |
Problems |
---|---|---|---|

Section
0 |
Sept.
8 |
18
-19 |
1, 2, 3, 4, 9, 11, 14, 18 |

Section
1.1 |
Sept.
20 |
38-40 |
2, 5, 6, 9, 10, 13, 16,
18, 20 |

Section
1.2 |
Sept.
27 |
52-53 |
1, 3, 4, 5, 7 |

Section
1.2 Section 1.3 |
Oct.
6 |
53 79 |
8, 9, 10, 11, 12 1, 2, 4, 6, 10 |

Section
1.3 |
Oct.
16 |
80-82 |
12, 13, 14, 15, 18, 19,
25, 30, 31 |

Section
2.1 |
Nov.
3 |
106 131 |
Prove Lemma 2.1 (without
looking at proof in book) 1, 2, 3, 4 |

Section
2.1 |
Nov.
17 |
131-132 |
5, 6, 8, 11, 12, 14, 15,
18, 20, 22 |

Section
2.1 |
Dec.
6 |
132-133 |
16, 17, 23, 24. 26 27,
28, 29 |