Torus fibrations and localization of index II

Abstract

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 family of finitely many open subsets, each of which has a structure of the total space of a torus bundle. Under an acyclic condition we define the index of the Dirac-type operator by using the Witten-type deformation, and show that the index has several properties, such as excision property and a product formula. In particular, we show that the index is localized on the compact set.

47 pages, 2 figures. To appear in Communications in Mathematical Physics

References in corpus (4)

• Essential self-adjointness of Schroedinger type operators on manifolds
• Local torus actions modeled on the standard representation
• Twisted K-theory and finite-dimensional approximation
• On Liftings of Local Torus Actions to Fiber Bundles

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• Cobordism invariance and the well-definedness of local index
• The equivariant local index of the reduced space in the symplectic cutting
• Equivariant local index