Questions tagged [elliptic-cohomology]
The elliptic-cohomology tag has no usage guidance.
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"High-concept" explanation for proof of a theorem of Ochanine?
See Akhil Mathew's notes on Ochanine's theorem for elliptic genera here and here.
Let $\phi: \Omega_{SO} \to \Lambda$ be a genus. We might ask when $\phi$ satisfies the following multiplicative ...
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How is an $S^1$-equivariant elliptic cohomology theory affected as we continuously vary the underlying elliptic curve?
Grojnowski constructs a $S^1$-equivariant cohomology theory over a complex elliptic curve $E$, designed to trivially satisfy: $$E^*_{S^1}(pt) = E$$
The functor $E^*_{S^1}(-)$ takes in a space $X$ ...
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Twisted equivariant modular forms?
I'd like to know where I can find information about a class of objects which I think deserve to be called twisted equivariant modular forms. Let me guess a definition, indicate how it can be made more ...
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How exactly does the Kreck-Stolz description of elliptic homology match the one by Totaro?
In
Kreck, Matthias; Stolz, Stephan, $\mathbf H\mathbf P^2$-bundles and elliptic homology, Acta Math. 171, No. 2, 231-261 (1993). ZBL0851.55007.
the $n$th elliptic homology group of a space $X$ is ...
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Borel vs genuine equivariant cohomology in quantum field theory
A lot of important work in quantum field theory involves Borel equivariant cohomology of certain geometric objects, usually with the goal of computing integrals over some complicated moduli stack. In ...
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Which one is the long version of the Segal Bourbaki seminar article that Nora Ganter refers to on her TMF literature list?
I mean the extremely useful literature list compiled by Nora Ganter. One of the entries there is
Segal: Bourbaki and the long version of the Bourbaki article
What I know is the version on numdam (...
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Does the theorem that genera vanishing on even-dim complex projective bundles are elliptic also apply for integral-valued genera?
Ochanine proved in this paper that for genera taking values in $\mathbb{Q}$-algebras, vanishing on even-dimensional projective bundles is equivalent to being an elliptic genus (i.e. a specialization ...
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Rigidity of the TMF-valued equivariant elliptic genus
Let me preface this question by saying that I wrote it at least in part to understand its statement. As such, I hope that the reader will excuse any mistakes.
$\DeclareMathOperator{\ind}{ind}\...
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Localization for generalized Borel cohomology
For both equivariant de Rham cohomology and equivariant K-theory (in the "naive" or Borel sense), we have localization formulae which allow us to compute this cohomology in terms of the ...