MATH4161 Algebraic Topology.
Michaelmas 2012
Lecturer: Andrew Lobb
Schedule:
Thursdays 9am-10am PCL053
Fridays 10am-11am PCL058
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), homotopy, contractibility, retractions, cell decompositions, Euler characteristic. |
2 |
Simplicial complexes, chain groups and differentials, simplicial homology groups. |
3 |
Simplicial homology, chain complexes, singular homology. |
4 |
Homotopy invariance, exact sequences of abelian groups. |
5 |
Long exact sequences in homology, homological algebra |
6 |
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Assignments
Solutions to any starred questions are to be handed in to my pigeonhole in the first floor common room in the mathematics department.
Exercise Sheet |
Date posted |
Date due |
Solutions |
|
12th October 2012 |
1st November 2012 |
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19th October 2012 |
1st November 2012 |
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26th October 2012 |
1st November 2012 |
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12th November 2012 |
12th December 2012 |
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20th November 2012 |
12th December 2012 |
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30th November 2012 |
12th December 2012 |