Stringy K-theory and stringy (quantum) cohomology for varieties with a finite group action.
by
Ralph Kaufmann
University of Connecticut, Department of Mathematics
Coauthors: Tyler Jarvis, Takashi Kimura

For a variety with an action of finite group G, we define stringy K-theory, stringy cohomology and provide a Chern character between them. The idea behind these constructions is that for a quotient by a finite group there is a stringy construction of all the usual functors which take values in Frobenius algebras. This is done by taking into account the fixed point sets of all group elements which yields a group graded object. On this stringy data there is an action by the group G and the invariants of this action additively yield the equivariant data, e.g. the G-equivariant K-theory of X. There is, however, a new stringy multiplication which respects the group grading.

One motivation for studying these stringy objects is that it is expected that the stringy invariants carry information about the possible desingularizations. This is for instance the case for a symmetric product of K3 surfaces and its resolution by the Hilbert scheme.

Date received: February 16, 2005