Course MA 448

K-theory and Solitons

Dr. Sergey Cherkis

Office: 19.31 Hamilton Building
Office Hours: e-mail for appointment
Phone: 01 896 3453

Homework Assignments:

Problem Set 1 Due 29 January 2009
Problem Set 2 Due 1pm 11 February
Problem Set 3 Due 10am 12 February
Problem Set 4 Due 10am 19 February
Problem Set 5 Due 10am 26 February

Problem Set 6 Due 1 pm 8 April
Problem Set 7 Due 1 pm 15 April

Note:

Friday, 30 January
Lectures 3.00 to 4.50
in Salmon Lecture Theatre

No lecture Wednesday, 7 January and
no lecture Wednesday, 14 January.

Reading Week:
All Lectures Wednesday, Nov. 5
from 11 to 2:30 (with a lunch break)
in the Meeting Room, Second Floor, School of Maths, Building 19.

No MA 448 lectures Wed. 22nd and Thur. 23 October.

No MA448 lectures this Thursday, 9 October.
Instead, a lecture 10 am on Friday, 10 October in the Seminar Room 2.6
(second floor on the School of Mathematics in Hamilton Building)

Lectures:

Wednesday	13.00-13.50	in	Synge Lecture Theatre
Thursday	10.00-11.50		Synge Lecture Theatre
	16.00-16.50		Salmon Lecture Teatre

Course Description:

Quick tour of Algebraic Topology
Cell Complexes, Homotopy, Homology and cohomology, Spectral Sequences

Vector Bundles and Associated Fiber Bundles

Characteristic Classes

Ring Structure of K(X)

Bott Periodicity

Division Algebras and Parallelizable Spheres

Dirac Operator and its Index

Textbooks:

Required:

1. Hajime Sato, “Algebraic Topology: An Intuitive Approach,”
Translations of Mathematical Monographs, Vol. 183
American Mathematical Society 1999
ISBN: 0-8218-1046-4

2. Allen Hatcher, “Vector Bundles and K-Theory,” download page.