Algebraic Topology I
(Math 261)
An introduction to algebraic topology.
Spring 2008
Instructor:
Paul Aspinwall
Credits: 1.00, Hours: 03.0
Time: Wednesdays and Fridays 2:50 - 4:05PM
Location: Physics 227
Requirements
Exams: A take home final due back at 5:00pm on Wednesday April 30.
Homework
Pictures
Click here to see a torus knot.
Prerequisits
Math 200 and 205, or consent from me.
Synopsis
A rough outline is as follows
- Introductory ideas
- Basic ideas of category theory
- Retractions
- Cell complexes
- Homotopy
- Homotopy of maps
- Fundamental group
- Van Kampen's Theorem
- Application to cell complexes
- Covering spaces
- Higher homotopy groups (very briefly)
- Homology
- Chain complexes
- Simplicial homology
- Singular homology
- Relative homology
- Homotopy invariance
- Excision
- Mayer-Vietoris Sequence
- Cellular Homology
- Eilenberg-Steenrod Axioms
- Homology with arbitrary coefficients
Textbooks
The course will be based on the text:
- A. Hatcher, Algebraic Topology I, Cambridge University
Press 2001 and available over
the web.
If you are going to print this it may be useful to
note that we will mainly only use chapters 0, 1 and 2 of Hatcher's book and
none of the "additional topics".
It may also be useful to refer to
- Edwin H. Spanier, Algebraic topology,
Springer-Verlag 1966.
- James R. Munkres, Topology: A First Course,
Prentice Hall, 1974.
- M. Greenberg and J. Harper, Algebraic Topology: A First
Course, Addison-Wesley 1981.
- William S. Massey, Algebraic topology: an introduction,
Springer-Verlag 1977.
- William S. Massey, A basic course in algebraic topology,
Springer-Verlag 1991.
- William S. Massey, Introduction to homology theory,
Yale 1977.
- William S. Massey, Singular homology theory,
Springer-Verlag 1980.
- William Fulton, Algebraic Topology: A First Course,
Srpinger-Verlag 1995.
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