An index theorem for end-periodic operators
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Mrowka_An index theorem.pdf
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Author(s)
Ruberman, Daniel
Saveliev, Nikolai
Mrowka, Tomasz S
Date Issued
September 2015
Journal
Compositio Mathematica
Publisher
Cambridge University Press
Citation
Mrowka, Tomasz, Daniel Ruberman, and Nikolai Saveliev. “An Index Theorem for End-Periodic Operators.” Compositio Mathematica 152.2 (2016): 399–444.
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. School of Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/S0010437X15007502
