Circle-equivariant classifying spaces and the rational equivariant sigma genus

Matthew Ando; J. P. C. Greenlees

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arXiv · 0705.2687

Circle-equivariant classifying spaces and the rational equivariant sigma genus

Matthew Ando·J. P. C. Greenlees

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Abstract

The circle-equivariant spectrum MString_C is the equivariant analogue of the cobordism spectrum MU<6> of stably almost complex manifolds with c_1=c_2=0. Given a rational elliptic curve C, the second author has defined a ring T-spectrum EC representing the associated T-equivariant elliptic cohomology. The core of the present paper is the construction, when C is a complex elliptic curve, of a map of ring T-spectra MString_C --> EC which is the rational equivariant analogue of the sigma orientation of Ando-Hopkins-Strickland. We support this by a theory of characteristic classes for calculation, and a conceptual description in terms of algebraic geometry. In particular, we prove a conjecture of the first author.

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BibTeX RIS

Matthew Ando, J. P. C. Greenlees. 2010-07-22. Circle-equivariant classifying spaces and the rational equivariant sigma genus. https://arxiv.org/abs/0705.2687

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