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In the previous papers, Furuta, Yoshida and the author gave a definition ofanalytic index theory of Dirac-type operator on open manifolds by making use ofsome geometric structure on an open covering of the end of the open manifoldand a perturbation of the Dirac-type operator. In this paper we show thecobordism invariance of the index, and as an application we show thewell-definedness of the index with respect to the choice of the open covering.

Cobordism invariance and the well-definedness of local index