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

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

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover [tilde over 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 transl...

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Bibliographic Details
Main Authors: Ruberman, Daniel (Author), Saveliev, Nikolai (Author), Mrowka, Tomasz S (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Mathematical Sciences Publishers, 2016-09-22T21:02:23Z.
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Summary:We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover [tilde over 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[subscript ∗] ([tilde over X])→H[subscript ∗] ([tilde over X]). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.
National Science Foundation (U.S.). (grant DMS-0805841)

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