Math Institute Oxford

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The Mathematical Institute is the mathematics department at the University of Oxford, England.

The institute was found in 1966.

Characteristic Classes
Trinity Term 2013

Christopher Douglas
Course Time: T10-12
Course Location: TCC
Email: cdouglas@maths

Course Outline
Tues. 23 Apr 1. Vector bundles.
Tues. 23 Apr 2. Classifying spaces.
Tues. 30 Apr 1. Crash course: Serre spectral sequences.
Tues. 30 Apr 2. Crash course: Eilenberg-Moore spectral sequences.
Tues. 7 May 1. Cohomology of real Grassmannians, mod 2.
Tues. 7 May 2. Stiefel–Whitney classes as obstructions.
Tues. 14 May 1. Stiefel–Whitney calculations and applications.
Tues. 14 May 2. Complex Grassmannians and Chern classes.
Tues. 21 May 1. Cohomology of real Grassmannians, low rank.
Tues. 21 May 2. Cohomology of real Grassmannians, adjoin 1
2 .
Tues. 28 May 1. Euler classes.
Tues. 28 May 2. Pontryagin classes.
Tues. 4 June 1. Characteristic classes as symmetric polynomials.
Tues. 4 June 2. Pontryagin classes of a complex bundle.
Tues. 11 June 1. Integral cohomology groups of real Grassmannians.
Tues. 11 June 2. Integral cohomology rings of real Grassmannians.
References
Milnor & Stasheff, Characteristic classes.
Hatcher, Algebraic topology, chapter 4.
Hatcher, Spectral sequences in algebraic topology.
Hatcher, Vector bundles and K-theory.
McCleary, A user’s guide to spectral sequences.
Weibel, An introduction to homological algebra.

Contact information:-
Mathematical Institute
24–29 St Giles'
Oxford
OX1 3LB
Address from 2/9/2013

Mathematical Institute
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Tel: +44 (0)1865 273525
Fax: +44 (0)1865 273583
Email: enquiries@maths.ox.ac.uk

Map:-

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