English

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

Algebraic Topology 2007-05-23 v1 Mathematical Physics math.MP Quantum Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.math/0101121,
  title  = {A renormalized Riemann-Roch formula and the Thom isomorphism for the free loop space},
  author = {Matthew Ando and Jack Morava},
  journal= {arXiv preprint arXiv:math/0101121},
  year   = {2007}
}

Comments

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