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

Tomasz Mrowka; Daniel Ruberman; Nikolai Saveliev

doi:10.2140/agt.2014.14.3689

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

Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	3689-3700
Number of pages	12
Journal	Algebraic and Geometric Topology
Volume	14
Issue number	6
DOIs	https://doi.org/10.2140/agt.2014.14.3689
State	Published - Jan 15 2015

Keywords

Alexander polynomial
Periodic end
de Rham complex

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2014.14.3689

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AU - Saveliev, Nikolai

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AB - 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.

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

Abstract

Keywords

ASJC Scopus subject areas

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