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arXiv · 1508.06793

K-theoretic invariants of Hamiltonian fibrations

Yasha Savelyev·Egor Shelukhin
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Abstract

We introduce new invariants of Hamiltonian fibrations with values in the suitably twisted K-theory of the base. Inspired by techniques of geometric quantization, our invariants arise from the family analytic index of a family of natural $Spin^c$-Dirac operators. As an application we give new examples of non-trivial Hamiltonian fibrations, that have not been previously detected by other methods. As one crucial ingredient we construct a potentially new homotopy equivalence map, with a certain naturality property, from $BU$ to the space of index $0$ Fredholm operators on a Hilbert space, using elements of modern theory of homotopy colimits.

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BibTeXRIS

Yasha Savelyev, Egor Shelukhin. 2019-01-18. K-theoretic invariants of Hamiltonian fibrations. https://arxiv.org/abs/1508.06793

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