Algebraic & Geometric Topology

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

Tomasz Mrowka, Daniel Ruberman, and Nikolai Saveliev

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We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X̃X. 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(X̃)H(X̃). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.

Article information

Algebr. Geom. Topol., Volume 14, Number 6 (2014), 3689-3700.

Received: 9 February 2014
Revised: 31 July 2014
Accepted: 26 August 2014
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58J20: Index theory and related fixed point theorems [See also 19K56, 46L80]
Secondary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} 58A12: de Rham theory [See also 14Fxx]

de Rham complex periodic end Alexander polynomial


Mrowka, Tomasz; Ruberman, Daniel; Saveliev, Nikolai. Index theory of the de Rham complex on manifolds with periodic ends. Algebr. Geom. Topol. 14 (2014), no. 6, 3689--3700. doi:10.2140/agt.2014.14.3689.

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