K-theory and localisation for non-commutative rings

Amnon Neeman – 21 February 2001

If R is a commutative ring and C is a multiplicative set of elements of R, we all know how to form the quotient ring C-1R, and it is classical that there is a long exact sequence in algebraic K-theory. In surgery, it turns out to be important to study the the analogue where the ring R is not commutative. The talk will begin with a survey of known results, by Schofield, Cohen, Vogell and many others. Ranicki asked me what Thomason's K-theory localisation result says about the subject. I will discuss our joint work.