Circle-equivariant classifying spaces and the rational equivariant sigma\n genus

2007/05/18 by Matthew Ando, Ando, Matthew, J. P. C. Greenlees +1
Mathematics · Physics and Astronomy · #55N34 #57R20 #57R85 #57R91 #58J26 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0705.2687

openalex publication_date 2007/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The circle-equivariant spectrum MString_C is the equivariant analogue of the\ncobordism spectrum MU<6> of stably almost complex manifolds with c₁=c₂=0.\nGiven a rational elliptic curve C, the second author has defined a ring\nT-spectrum EC representing the associated T-equivariant elliptic cohomology.\nThe core of the present paper is the construction, when C is a complex elliptic\ncurve, of a map of ring T-spectra\n MString_C --> EC which is the rational equivariant analogue of the sigma\norientation of Ando-Hopkins-Strickland. We support this by a theory of\ncharacteristic classes for calculation, and a conceptual description in terms\nof algebraic geometry. In particular, we prove a conjecture of the first\nauthor.\n

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