A renormalized Riemann-Roch formula and the Thom isomorphism for the free loop space

Details A renormalized Riemann-Roch formula and the Thom isomorphism for the free loop space A renormalized Riemann-Roch formula and the Thom isomorphism for the free loop space

2001-01-14

arxiv.org/abs/math/0101121v1

Mathematics

Algebraic Topology

to appear in Contemporary Math. [The Milgram Festschrift, ed. A. Adem, R. Cohen, G. Carlsson]

Scientific paper

Let E be a circle-equivariant complex-orientable cohomology theory. We show that the fixed-point formula applied to the free loopspace of a manifold X can be understood as a Riemann-Roch formula for the quotient of the formal group of E by a free cyclic subgroup. The quotient is not representable, but (locally at p) its p-torsion subgroup is, by a p-divisible group of height one greater than the formal group of E.

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