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    block this user Liviu Nicolaescu Trusted member

    Assistant Professor

    University of Notre Dame

    On the cobordism invaraince of the index of Dirac operators

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    Abstract. We describe a tunneling proof of the cobordism invariance of the index of Dirac operators. The goal of this note is to present a very short proof of the cobordism invariance of the index. More precisely, if D is a Dirac operator on an odd dimensional manifold M with boundary ? M = M then we show that the index of its restriction D to M is zero. The novelty of this proof consists in the fact that we provide an explicit isomorphism between the kernel and the cokernel of D. This map can be viewed as a sort of propagator (see Sect. 4). 1. The setting Consider the following collection of data.

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    Title : On the cobordism invaraince of the index of Dirac operators
    Author(s) : Liviu I. Nicolaescu
    Abstract : Abstract. We describe a tunneling proof of the cobordism invariance of the index of Dirac operators. The goal of this note is to present a very short proof of the cobordism invariance of the index. More precisely, if D is a Dirac operator on an odd dimensional manifold M with boundary ? M = M then we show that the index of its restriction D to M is zero. The novelty of this proof consists in the fact that we provide an explicit isomorphism between the kernel and the cokernel of D. This map can be viewed as a sort of propagator (see Sect. 4). 1. The setting Consider the following collection of data.
    Keywords : Dirac operators, index, cobordism

    Subject : unspecified
    Area : Mathematics
    Language : English
    Affiliations :  University of Notre Dame
    Url : http://www.nd.edu/~lnicolae/index-cobordism.pdf
    Doi : 10.1.1.70.3422

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