An index theorem for end-periodic operators

Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)399-444
Number of pages46
JournalCompositio Mathematica
Issue number2
StatePublished - Feb 1 2016


  • Fredholm operator
  • Index theorem
  • periodic end
  • positive scalar curvature

ASJC Scopus subject areas

  • Algebra and Number Theory


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