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Bott periodicity and stable quantum classes

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Abstract

We use Bott periodicity to relate previously defined quantum classes to certain “exotic Chern classes” on \(BU\). This provides an interesting computational and theoretical framework for some Gromov–Witten invariants connected with cohomological field theories. This framework has applications to study of higher dimensional, Hamiltonian rigidity aspects of Hofer geometry of \( \mathbb{CP }^{n}\), one of which we discuss here.

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Acknowledgments

I would like to thank Leonid Polterovich and Tel Aviv university for inviting me, and providing with a friendly atmosphere in which to undertake some thoughts that led to this article. In particular I am grateful to Leonid for compelling me to think about Gromov K-area. I also Alexander Givental, Leonid and Dusa McDuff for comments on organization and content, the anonymous referee for some brilliant comments and suggestions, and Ralph Cohen for providing an important reference.

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  1. Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montreal, QC, H3C 3J7, Canada

    Yasha Savelyev

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  1. Yasha Savelyev
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Correspondence to Yasha Savelyev.

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Savelyev, Y. Bott periodicity and stable quantum classes. Sel. Math. New Ser. 19, 439–460 (2013). https://doi.org/10.1007/s00029-012-0101-7

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