MATH 8307: Algebraic Topology (Spring 2015) |

Lecturer: Craig Westerland, 459 Vincent Hall, 612-625-0523, cwesterl@umn.edu.

Lecture: 11:15 -- 12:05 Monday, Wednesday, Friday, Vincent Hall 209.

Office Hours: Wednesday 1:30 -- 2:30, 3:30 -- 4:30, Friday 1:30 -- 2:30.

This is a second course in algebraic topology; students will be assumed to be familiar with the basics of homology, cohomology, and fundamental groups. I will aim to focus on parts of algebraic topology that, while part of topology in its own right, are essential to differential and algebraic geometry, e.g.: Poincaré duality, Grassmannians, vector bundles, K-theory, cobordism, characteristic classes, and obstruction theory. The foundations of this subject are, however, in pure homotopy theory: (co)fibrations, homotopy extension and lifting properties, homotopy groups, Eilenberg-MacLane spaces, Whitehead and Hurewicz theorems, Postnikov towers.

- Allen Hatcher, Algebraic Topology.
- Peter May, A Concise Course in Algebraic Topology.
- Haynes Miller, Notes on Cobordism.
- Chuck Weibel, The K-book, in particular section 4.2 on the classifying space of a small category.
- Steve Mitchell, Notes on principal bundles, in particular sections 6 and 7.
- John Milnor and Jim Stasheff, Characteristic Classes.

Will consist of irregularly assigned homework:

- First Homework, due 4 March.
- Second Homework, due 7 April.

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