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.

Goals and Objectives

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.

References

• 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.

Assessment

Will consist of irregularly assigned homework:

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