Torus fibrations and localization of index I
Symplectic Geometry
2010-09-03 v7 Differential Geometry
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.
Cite
@article{arxiv.0804.3258,
title = {Torus fibrations and localization of index I},
author = {Hajime Fujita and Mikio Furuta and Takahiko Yoshida},
journal= {arXiv preprint arXiv:0804.3258},
year = {2010}
}
Comments
23 pages. 2 figures. Errors corrected. The title changed. Corollary 6.12 and references added