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An index theorem for end-periodic operators

Published online by Cambridge University Press:  07 September 2015

Tomasz Mrowka
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA email [email protected]
Daniel Ruberman
Affiliation:
Department of Mathematics, MS 050, Brandeis University, Waltham, MA 02454, USA email [email protected]
Nikolai Saveliev
Affiliation:
Department of Mathematics, University of Miami, PO Box 249085, Coral Gables, FL 33124, USA email [email protected]

Abstract

We extend the Atiyah, Patodi, and Singer index theorem for first-order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes’ Fredholm theory for general end-periodic operators. Our index theorem is expressed in terms of a new periodic eta-invariant that equals the Atiyah–Patodi–Singer eta-invariant in the cylindrical setting. We apply this periodic eta-invariant to the study of moduli spaces of Riemannian metrics of positive scalar curvature.

Type
Research Article
Copyright
© The Authors 2015 

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