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Cobordism invariance and the well-definedness of local index

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Abstract

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

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Acknowledgments

The author would like to thank Mikio Furuta and Takahiko Yoshida for stimulating discussions. Partly supported by Grant-in-Aid for Young Scientists (B) 23740059 and Young Scientists (B) 26800045

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Authors and Affiliations

  1. Department of Mathematical and Physical Sciences, Japan Women’s University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo, 112-8681, Japan

    Hajime Fujita

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  1. Hajime Fujita
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Correspondence to Hajime Fujita.

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Fujita, H. Cobordism invariance and the well-definedness of local index. Ann Glob Anal Geom 47, 399–414 (2015). https://doi.org/10.1007/s10455-015-9452-6

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  • DOI: https://doi.org/10.1007/s10455-015-9452-6

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