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

Matthew Ando, Jack Morava

Published 2001-01-14Version 1

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.

Comments: to appear in Contemporary Math. [The Milgram Festschrift, ed. A. Adem, R. Cohen, G. Carlsson]
Categories: math.AT, math-ph, math.MP, math.QA
Subjects: 57R91, 55N20, 14L05, 19L10, 55P92
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