MATH4161 Algebraic Topology.
Michaelmas 2013
Lecturer: Andrew Lobb
Schedule:
Monday 9am-10am CM225a
Wednesday 9am-10am CM225a
Books
There are many books called something like An Introduction to Algebraic Topology or just Algebraic Topology. Any of these will cover most if not all of what you shall see during this course. It's really a matter of personal taste as to which books you prefer. However, a book that is currently very popular (and available for free complete download on the author's website) is that of Hatcher's. Here are some other authors worth a look:
Armstrong;
Bredon;
Dold;
Fulton;
Spanier.
Lectures
Here's a brief outline of what I intend to cover in each week's lectures.
Week |
Content |
1 |
CW-complexes (otherwise known as cell complexes), cellular homology. |
2 |
Examples of cellular homology, beginnings of homological algebra. |
3 |
Simplicial homology, chain complexes in general. |
4 |
Singular homology, functoriality. |
5 |
Homotopy recap, homotopy invariance, using homology as more than just an invariant. |
6 |
Homological algebra, short five lemma, SES of chain groups gives LES of chain complexes. |
7 |
LES of a pair, equivalence of simplicial and singular homology. |
8 |
LES of a pair, equivalence of cellular and singular homology. |
9 |
Mayer-Vietoris, computations, applications. |
10 |
More computations and applications, other coefficient rings. |
Assignments
Solutions to any starred questions are to be handed in to my pigeonhole in the first floor common room in the mathematics department on the due date, or alternatively to me in lecture.
Exercise Sheet |
Date posted |
Date due |
Solutions |
7th October 2013 |
14th October 2013 |
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14th October 2013 |
21st October 2013 |
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22nd October 2013 |
30th October 2013 |
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4th November 2013 |
11th November 2013 |
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11th November 2013 |
18th November 2013 |
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21th November 2013 |
27th November 2013 |
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5th December 2013 |
11th December 2013 |