Algebraic K-Theory and Applications to Topology
Student No.:40
Time:Mon & Wed 15:20-16:55, Sep.17-Dec.12
Instructor:Thomas Farrell  [Tsinghua University]
Place:Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2018-9-17
Ending Date:2018-12-12

We will proceed chronologically from Whitehead torsion and the projective Class group (K_1 and K_a) to Bass's lower K-theory (K_n for n<0) and then to Quillen's higher K-groups (K_n for n>1). Topological application include the s-cobordism theorem,manifold compactifications and pseudo-isotopy theory.

A basic course in algebraic topology through the universal coefficient theorem and cup products, plus basic facts about smooth manifolds including the Whitney embedding theorem and Sard's theorem.

[1] H.Bass's book : Algebraic K-theory;
[2] J. Milnor's 1966 BAMS expository article: Whitehead torsion ,vol 72, pp 358-426;
[3] Marshall Cohen’s book: A course on simple homotopy theory;
[4] J.Rosenberg's book: algebraic K-theory and its applications.