Topology III Course Information
Department of Mathematics University of Cincinnati
Topology III (15-Math-606-001) Winter Quarter 2004
Instructor Prof. David A. Herron (813 Old Chem Bldg, 556-4075) Office Hours: M,W,F 10-11
Textbooks There are a slew of books on reserve (under my name) in the library. Here are the primary texts which I will use to generate my lectures. It's a good idea to look at more than one book, because often some author will say things in just the right way....
- Mu Topology (second edition) by Munkres
- B Topology and Geometry by Bredon
- GP Differential Topology by Guillemin and Pollack
- Ma Algebraic Topology: An Introduction by Massey
- S An Introduction to Topology and Homotopy by Sieradski
General Syllabus Chapters: 11,13 in Mu; II,III in B; 1 in GP; 4,5 in Ma; 12,14 in S
This page is a work in progress!
Below I list information regarding: this week's hot topics , suggested problems, homework.
29/3-2/4 This week we begin our study of the Seifert-Van Kampen theorem. We'll have to remember/learn a bunch of algebraic stuff like: free groups, free products, amalgamation. I really like the book by Massey, altho Sieradski is ok too.
5-9 April This week we continue our study of the Seifert-Van Kampen theorem. After proving this bad boy, we'll look at several examples including the fundamental groups of wedges of circles and of certain compact surfaces.
12-16 April This week we return to our study of covering spaces and use our knowledge about fundamental groups to understand covering spaces.
19-23 April
26-30 April
3-7 May
10-14 May
17-24 May
24-28 May
31 May-4 June During our last week we
Here are suggested problems for each indicated section.
- 67, Free Abelian Groups, p.412: 4
- 68, Free Products of Groups, p.412: 2,3
- 69, Free Groups, p.425: 1,3
- 70, Seifert-Van Kampen Theorem, p.433: 1,2,3
- 71, Wedge of Circles, p.438: 1,2,3,4,5
- 72,73,74, Compact Surfaces , p.445:1,2; pp.453-454:1-7
- 79, Equivalence of Covering Spaces, p.483:1-5
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Here is the assigned homework with due dates.
| Due Dates | Page:Problem |
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| 7,9 Jan |
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| 12,14,16 Jan |
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| 21,23 Jan |
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| 26,28 Jan |
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| 4,6 Feb |
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| 9,11,13 Feb |
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Midterm |
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| 16,18,20 Feb |
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| 23,25,27 Feb |
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| 1,3,5 Mar |
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| 8,10,12 Mar |
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| 17 March |
Final Exam 8-10 |