On Algebraic K-Theroy of Real Algebraic Varieties with Circle Action
by
Yildiray Ozan
Middle East Technical University, Mathematics Department

Assume that X is a compact connected nonsingular real algebraic variety with an algebraic S¹-action and \pi: X --> B = X/S¹ is the quotient map. In this note, we will show that if the S¹-action is free, then after tensoring with Q, the reduced Grothendieck K-group, [K\tilde]₀(R(X, C))\otimesQ of X, where R(X, C)=R(X)\otimesC, R(X) denoting the ring of entire rational (regular) functions on the real algebraic variety X, lies in the image of \pi^*:[K\tilde]₀(B)\otimesQ --> [K\tilde]₀(X)\otimesQ. This extends partially the result of Bochnak and Kucharz that if X=Y×S¹, where Y is also a real algebraic variety, then [K\tilde]₀(R(X, C))=[K\tilde]₀(R(Y, C)). As an application we will show that for a compact connected Lie group G [K\tilde]₀(R(G, C))\otimesQ=0.

Date received: July 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeh-60.