Torus fibrations and localization of index II-Local index for acyclic compatible system -

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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