Event time:
Thursday, October 16, 2014 - 12:30pm to 1:30pm
Location:
431 DL
Speaker:
Dave Anderson
Speaker affiliation:
IMPA
Event description:
The bivariant machinery of Fulton-MacPherson gives a way to associate an operational cohomology theory to any homology theory on varieties. Part of their motivation was to find a formal cohomology ring to associate with Chow homology, since no other geometrically meaningful option was available, and to use this formalism in proving Riemann-Roch theorems. In joint work with Sam Payne, we apply this machine to the K-homology of coherent sheaves to get an operational K-theory, denoted opK(X). This agrees with the usual K-theory of vector bundles when X is smooth but is different in general. I will explain some of the basic properties of opK, and also how to use it to obtain new information about usual K-theory.