Volume 14, issue 6 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Index theory of the de Rham complex on manifolds with periodic ends

Tomasz Mrowka, Daniel Ruberman and Nikolai Saveliev

Algebraic & Geometric Topology 14 (2014) 3689–3700
Abstract

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

Keywords
de Rham complex, periodic end, Alexander polynomial
Mathematical Subject Classification 2010
Primary: 58J20
Secondary: 57Q45, 58A12
References
Publication
Received: 9 February 2014
Revised: 31 July 2014
Accepted: 26 August 2014
Published: 15 January 2015
Authors
Tomasz Mrowka
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
USA
Daniel Ruberman
Department of Mathematics
MS 050
Brandeis University
Waltham, MA 02454
USA
Nikolai Saveliev
Department of Mathematics
University of Miami
PO Box 249085
Coral Gables, FL 33124
USA