An index theorem for end-periodic operators
Author(s)Ruberman, Daniel; Saveliev, Nikolai; Mrowka, Tomasz S
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. School of Science
Cambridge University Press
Mrowka, Tomasz, Daniel Ruberman, and Nikolai Saveliev. “An Index Theorem for End-Periodic Operators.” Compositio Mathematica 152.2 (2016): 399–444.