Index theory of the de Rham complex on manifolds with periodic ends
Name
Mrowka_Index theory.pdf
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126.7 KB
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73082b5f0a21c8a0369fed7c83683cc7
Author(s)
Ruberman, Daniel
Saveliev, Nikolai
Mrowka, Tomasz S
Date Issued
January 2015
Journal
Algebraic & Geometric Topology
Publisher
Mathematical Sciences Publishers
Citation
Mrowka, Tomasz, Daniel Ruberman, and Nikolai Saveliev. “Index Theory of the de Rham Complex on Manifolds with Periodic Ends.” Algebraic & Geometric Topology 14.6 (2015): 3689–3700.
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.2140/agt.2014.14.3689
