Geodesic
Index theory of the de Rham complex on manifolds with periodic ends
Mrowka, Tomasz1 ; Ruberman, Daniel2 ; Saveliev, Nikolai3
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2Department of Mathematics, MS 050, Brandeis University, Waltham, MA 02454, USA
3Department of Mathematics, University of Miami, PO Box 249085, Coral Gables, FL 33124, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3689-3700
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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.

DOI : 10.2140/agt.2014.14.3689
Classification : 58J20, 57Q45, 58A12
Keywords: de Rham complex, periodic end, Alexander polynomial

Mrowka, Tomasz  1   ; Ruberman, Daniel  2   ; Saveliev, Nikolai  3

1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2 Department of Mathematics, MS 050, Brandeis University, Waltham, MA 02454, USA
3 Department of Mathematics, University of Miami, PO Box 249085, Coral Gables, FL 33124, USA 
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Mrowka, Tomasz; Ruberman, Daniel; Saveliev, Nikolai. Index theory of the de Rham complex on manifolds with periodic ends. Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3689-3700. doi: 10.2140/agt.2014.14.3689

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