Spectral multiplicity and odd K-theory-II

Details Spectral multiplicity and odd K-theory-II Spectral multiplicity and odd K-theory-II

2012-01-31

arxiv.org/abs/1201.6678v2

Mathematics

K-Theory and Homology

References and misprints corrected

Scientific paper

Let {D_x} be a family of unbounded self-adjoint Fredholm operators representing an element of K^1(M). Consider the first two components of the Chern character of the family. It is known that these correspond to the spectral flow of the family and the index gerbe. In this paper we consider descriptions of these classes, both of which are in the spirit of holonomy. These are then studied for families parametrized by a closed 3-manifold. A connection between the multiplicity of the spectrum (and how it varies) and these classes is developed.

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