The chiral index of the fermionic signature operator

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.

Received 29 April 2014

Accepted 7 September 2015

Published 7 June 2017