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An integer valued topological index of a Dirac operator is introduced for apair of a 4n+2 dimensional open Spin^c manifold and a section of thedeterminant line bundle satisfying some property. We show a relation betweenthe index and an index of a Dirac operator of its characteristic submanifold,by a localization of K-class.

Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c Manifolds