Torus fibrations and localization of index II

Details Torus fibrations and localization of index II Torus fibrations and localization of index II

2009-10-02

arxiv.org/abs/0910.0358v3

Mathematics

Differential Geometry

50 pages, 2 figures. Definition 4.1 corrected

Scientific paper

We give a framework of localization for the index of a Dirac-type operator on an open manifold. Suppose the open manifold has a compact subset whose complement is covered by a finitely many open subset, each of which has a structure of the total space of a torus bundle. Under a certain compatibility condition and acyclicity we show that the index of the Dirac-type operator is localized on the compact set.

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