Professor Alexandru I. Suciu

MTH 3483 - Topics in Topology

Bundles and Characteristic Classes

Fall 1998

Course Information

Course:	MTH 3483--Topics in Topology
Instructor:	Alex Suciu
Time and Place:	Mon. & Wed., 7:15 - 8:45 PM, in 544 NI
Office Hours:	Mon. & Wed., 4:00 - 5:00 PM, in 441 LA
Prerequisites:	MTH 3105--Topology I, MTH 3107--Topology II, MTH 3400--Geometry I, MTH 3481--Topology III.
Textbooks:	Fibre Bundles, by Dale Husemoller Characteristic Classes, by John Milnor and James Stasheff
Grade:	Based on problem sets and class participation

Course Description

The course is meant as an introduction to fiber bundles and characteristic classes. It supposes a certain familiarity with the basic objects of topology and geometry, e.g., manifolds, cell complexes, homology and homotopy.

We will first discuss principal bundles (Milnor's construction of universal bundles, the homotopy classification of G-bundles) and vector bundles (new vector bundles out of old ones, local coordinate description). We will work out many examples, e.g., bundles over spheres, Lie groups and homogeneous manifolds, gauge groups.

We will then study the cohomology of classifying spaces, i.e., characteristic classes: Grassmann manifolds and Stiefel-Whitney classes; oriented bundles, obstructions, Gysin and Wang sequences, the Thom isomorphism, and the Euler class; complex bundles, Chern classes, and Pontrjagin classes. Applications will include obstructions to embeddings of manifolds, vector fields on spheres, cobordism theory, Hirzebruch index formula, exotic spheres.

Homework Assignments

Notes & Homework 1		DVI		PDF
Homework 2	HTML	DVI	PS	PDF
Homework 3		DVI		PDF

Department of Mathematics	Office:	441 Lake Hall	Messages:	(617) 373-2450
Northeastern University	Phone:	(617) 373-4456	Fax:	(617) 373-5658
Boston, MA, 02115	Email:	alexsuciu@neu.edu	Directions

Created: August 20, 1998 Last modified: December 27, 1998
URL: http://www.math.neu.edu/~suciu/mth3483/toptop.f98.html