Differential Equivariant K-Theory

Details Differential Equivariant K-Theory Differential Equivariant K-Theory

2009-05-04

arxiv.org/abs/0905.0476v2

Mathematics

Algebraic Topology

64 pages; corrected the discussion of ring structure

Scientific paper

Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also construct a pushforward map which parallels the topological pushforward in equivariant K-theory. An analytic formula for the pushforward to the differential equivariant K-theory of a point is conjectured, and proved in the boundary case, in the case of a free action, and for ordinary differential K-theory in general. The latter proof is due to K. Klonoff.

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