Abstract
We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover 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*(X)→H*(X). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3689-3700 |
| Number of pages | 12 |
| Journal | Algebraic and Geometric Topology |
| Volume | 14 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jan 15 2015 |
Fingerprint
Keywords
- Alexander polynomial
- de Rham complex
- Periodic end
ASJC Scopus subject areas
- Geometry and Topology
Cite this
Index theory of the de Rham complex on manifolds with periodic ends. / Mrowka, Tomasz; Ruberman, Daniel; Saveliev, Nikolai.
In: Algebraic and Geometric Topology, Vol. 14, No. 6, 15.01.2015, p. 3689-3700.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Index theory of the de Rham complex on manifolds with periodic ends
AU - Mrowka, Tomasz
AU - Ruberman, Daniel
AU - Saveliev, Nikolai
PY - 2015/1/15
Y1 - 2015/1/15
N2 - We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover 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*(X)→H*(X). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.
AB - We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover 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*(X)→H*(X). We calculate the index of this weighted de Rham complex for all weights away from the exceptional ones.
KW - Alexander polynomial
KW - de Rham complex
KW - Periodic end
UR - http://www.scopus.com/inward/record.url?scp=84922308676&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84922308676&partnerID=8YFLogxK
U2 - 10.2140/agt.2014.14.3689
DO - 10.2140/agt.2014.14.3689
M3 - Article
AN - SCOPUS:84922308676
VL - 14
SP - 3689
EP - 3700
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 6
ER -