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The sigma orientation for analytic circle-equivariant elliptic cohomology. (English) Zbl 1021.55004
The author studies in detail the circle-equivariant elliptic cohomology theory constructed by I. Grojnowski (unpublished). It seems that the main achievement of the author is a construction of a canonical Thom class for a certain class of \(S^1\)-equivariant vector bundles: this class generalizes the sigma-orientation constructed by M. Ando, M. J. Hopkins and N. P. Strickland [Invent. Math. 146, No. 3, 595–687 (2001; Zbl 1031.55005)].

MSC:
55N34 Elliptic cohomology
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
57R91 Equivariant algebraic topology of manifolds
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References:
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