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arXiv · 0804.3258

Torus fibrations and localization of index I

Hajime Fujita·Mikio Furuta·Takahiko Yoshida
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Abstract

We define a local Riemann-Roch number for an open symplectic manifold when a complete integrable system without Bohr-Sommerfeld fiber is provided on its end. In particular when a structure of a singular Lagrangian fibration is given on a closed symplectic manifold, its Riemann-Roch number is described as the sum of the number of nonsingular Bohr-Sommerfeld fibers and a contribution of the singular fibers. A key step of the proof is formally explained as a version of Witten's deformation applied to a Hilbert bundle.

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Hajime Fujita, Mikio Furuta, Takahiko Yoshida. 2010-09-02. Torus fibrations and localization of index I. https://arxiv.org/abs/0804.3258

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