Back to Departmental Colloquium: Spring 2000
Departmental Colloquium
Date: Monday, Apr 10, 2000
Time: 4:15PM
Location: JWB 335
Angelo Vistoli
Bologna, Italy)
Title |
Decomposing equivariant K-theory rings |
Abstract |
Vector bundles are among the basic objects of study in all of geometry. Out of vector bundles on an algebraic variety or a topological space X one forms a ring K_0(X), the K -theory ring of X, introduced by Grothendieck. If furthermore there is a group G operating on X one forms the equivariant K -theory ring K_0(X,G), using equivariant vector bundles on X. For example if X is a point then K_0(X,G) is the representation ring of G, already a very interesting object. The ring K_0(X,G) has some of the same formal properties of the nonequivariant ring K_0(X), but its theory is richer, because of the interaction of the algebra coming from G with the geometry coming from X. In particular K_0(X,G) tends to decompose in interesting ways, reflecting the properties of the fixed point subsets. I will start by motivating the introduction of the K -theory rings, and end by illustrating some decomposition results in their simplest context. |
Algebraic K-theory
Representation Theory
Algebraic Geometry