TheWitten genus and equivariant elliptic cohomology
نویسندگان
چکیده
We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a new proof of the rigidity of theWitten genus, which exhibits a close relationship to recent work on non-equivariant orientations of elliptic spectra.
منابع مشابه
Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملDiscrete Torsion for the Supersingular Orbifold Sigma Genus
The first purpose of this paper is to examine the relationship between equivariant elliptic genera and orbifold elliptic genera. We apply the character theory of [HKR00] to the Borel-equivariant genus associated to the sigma orientation of [AHS01] to define an orbifold genus for certain total quotient orbifolds and supersingular elliptic curves. We show that our orbifold genus is given by the s...
متن کاملCircle-equivariant Classifying Spaces and the Rational Equivariant Sigma Genus
We analyze the circle-equivariant spectrum MStringC which is the equivariant analogue of the cobordism spectrum MU〈6〉 of stably almost complex manifolds with c1 = c2 = 0. In [Gre05], the second author showed how to construct the ring T-spectrum EC representing the T-equivariant elliptic cohomology associated to a rational elliptic curve C. In the case that C is a complex elliptic curve, we cons...
متن کاملRational S 1 - Equivariant Elliptic Cohomology
We give a functorial construction of a rational S 1-equivariant cohomology theory from an elliptic curve equipped with suitable coordinate data. The elliptic curve may be recovered from the cohomology theory; indeed, the value of the cohomology theory on the compactification of an S 1-representation is given by the sheaf cohomology of a suitable line bundle on the curve. The construction is eas...
متن کاملA Renormalized Riemann-roch Formula and the Thom Isomorphism for the Free Loop Space
Abstract. We show that the fixed-point formula in an equivariant complex-oriented cohomology theory E, applied to the free loop space of a manifold X, defines a (renormalized) Riemann-Roch formula for the quotient of the group law of E by a free cyclic subgroup. If E is K-theory, this explains how the elliptic genus associated to the Tate elliptic curve emerges from Witten’s analysis of the fix...
متن کامل