Torus Fibrations and Localization of Index I - Polarization and Acyclic Fibrations

被引：0

作者：

Fujita, Hajime ^{[1
]}

Furuta, Mikio ^{[2
]}

Yoshida, Takahiko ^{[3
]}

机构：

[1] Gakushuin Univ, Dept Math, Toshima Ku, Tokyo 1718588, Japan

[2] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1539814, Japan

[3] Meiji Univ, Grad Sch Sci & Technol, Dept Math, Tama Ku, Kawasaki, Kanagawa 2148571, Japan

来源：

JOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO | 2010年 / 17卷 / 01期

关键词：

Geometric quantization; index theory; localization; GEOMETRIC-QUANTIZATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a local Riemann-Roch number for an open symplectic manifold when a completely 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.

引用

页码：1 / 26

页数：26

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