Index theory of the de Rham complex on manifolds with periodic ends

Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X→X. The completion of this complex in exponentially weighted L2 norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H*(X)→H*(X). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.

Original languageEnglish (US)
Pages (from-to)3689-3700
Number of pages12
JournalAlgebraic and Geometric Topology
Volume14
Issue number6
DOIs
StatePublished - Jan 15 2015

Keywords

  • Alexander polynomial
  • de Rham complex
  • Periodic end

ASJC Scopus subject areas

  • Geometry and Topology

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