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

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arXiv · 1310.4246

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

Tomasz Mrowka·Daniel Ruberman·Nikolai Saveliev

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Abstract

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \to H_*(X'). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.

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Tomasz Mrowka, Daniel Ruberman, Nikolai Saveliev. 2013-10-16. Index theory of the de Rham complex on manifolds with periodic ends. https://doi.org/10.2140/agt.2014.14.3689

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