Professor Alexandru I. Suciu

MTH G722 · Readings in Algebraic Topology

Introduction to Homotopy Theory

Spring 2005

This course is meant as an introduction to classical Homotopy Theory, and some of its applications.

Here are some of the topics we may cover: Higher homotopy groups, cofibrations, fibrations, fiber bundles, homotopy sequences, homotopy groups of Lie groups and associated manifolds, cellular approximation, Hurewicz theorem, Whitehead theorem, Eilenberg-MacLane spaces, obstruction theory, Postnikov towers, cohomology of fiber bundles, characteristic classes, spectral sequences, Steenrod sqaures.

And here are some useful textbooks (including some olden goldies):

• Algebraic Topology, by Allen Hatcher, Cambridge University Press, 2002. Math Review.
• Topology and Geometry, by Glen Bredon, GTM No. 139, Springer-Verlag, 1997. Math Review.
• Elements of Homotopy Theory, by George W. Whitehead, GTM No. 61, Springer-Verlag, 1979. Math Review.
• Characteristic Classes, by John W. Milnor and James Stasheff, Ann. Math. Studies, No. 76, Princeton University Press, 1973. Math Review.
• Algebraic Topology, by Edwin H. Spanier, Corrected reprint, Springer-Verlag, 1981. Math Review.
• The topology of fibre bundles , by Norman Steenrod, reprint of 1951 edition, Princeton University Press, 1999. Math Review.
• Spectral Sequences in Algebraic Topology, by Allen Hatcher, draft book (Chapter 1), 2004.
• A user's guide to spectral sequences, by John McCleary, second edition, Cambridge Studies in Advanced Math, no. 58, Cambridge University Press, 2001. Math Review.