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

Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

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Index Theory
Weighted Norm
Smooth Manifold
Completion
Covering
Cover
Eigenvalue
Calculate

Keywords

  • Alexander polynomial
  • de Rham complex
  • Periodic end

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Index theory of the de Rham complex on manifolds with periodic ends. / Mrowka, Tomasz; Ruberman, Daniel; Saveliev, Nikolai.

In: Algebraic and Geometric Topology, Vol. 14, No. 6, 15.01.2015, p. 3689-3700.

Research output: Contribution to journalArticle

Mrowka, Tomasz ; Ruberman, Daniel ; Saveliev, Nikolai. / Index theory of the de Rham complex on manifolds with periodic ends. In: Algebraic and Geometric Topology. 2015 ; Vol. 14, No. 6. pp. 3689-3700.
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