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Two-cocycle twists and Atiyah–Patodi–Singer index theory

Published online by Cambridge University Press:  22 August 2018

SARA AZZALI  and
CHARLOTTE WAHL
SARA AZZALI
Affiliation:
Institut für Mathematik, Universität Potsdam, Karl–Liebknecht Str. 24-25, 14476 Golm, Germany. e-mail: azzali@uni-potsdam.de
CHARLOTTE WAHL
Affiliation:
Leibniz–Archiv, Waterloostr. 8, 30169 Hannover, Germany. e-mail: wahlcharlotte@gmail.com
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Abstract

We construct η- and ρ-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah–Patodi–Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 3 , November 2019 , pp. 437 - 487
Copyright
Copyright © Cambridge Philosophical Society 2018 

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