The Universal Gerbe and Local Family Index Theory
نویسندگان
چکیده
The goal of this paper is to apply the universal gerbe developed in [CMi1] and [CMi2] and the local family index theorems to give a unified viewpoint on the known examples of geometrically interesting gerbes, including the determinant bundle gerbes in [CMMi1], the index gerbe in [L] for a family of Dirac operators on odd dimensional closed manifolds. We also discuss the associated gerbes for a family of Dirac operators on odd dimensional manifolds with boundary, and for a pair of Melrose-Piazza’s Cl(1)-spectral sections for a family of Dirac operators on even dimensional closed manifolds with vanishing index in K-theory. The common feature of these bundle gerbes is that there exists a canonical bundle gerbe connection whose curving is given by the degree 2 part of the even eta-form (up to an exact form) arising from the local family index theorem.
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On the Relationship of Gerbes to the Odd Families Index Theorem
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