Mathematical Research Letters

Volume 24 (2017)

Number 1

The chiral index of the fermionic signature operator

Pages: 37 – 66

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n1.a3

Author

Felix Finster (Fakultät für Mathematik, Universität Regensburg, Germany)

Abstract

We define an index of the fermionic signature operator on evendimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators thereon for which our index is non-trivial.

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Supported in part by the Deutsche Forschungsgemeinschaft.

Paper received on 29 April 2014.