Friedl, Stefan and Lueck, Wolfgang (2017) Universal L-2-torsion, polytopes and applications to 3-manifolds. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 114. pp. 1114-1151. ISSN 0024-6115, 1460-244X
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Given an L2-acyclic connected finite CW-complex, we define its universal L2-torsion in terms of the chain complex of its universal covering. It takes values in the weak Whitehead group Whw(G). We study its main properties such as homotopy invariance, sum formula, product formula and Poincare duality. Under certain assumptions, we can specify certain homomorphisms from the weak Whitehead group Whw(G) to abelian groups such as the real numbers or the Grothendieck group of integral polytopes, and the image of the universal L2-torsion can be identified with many invariants such as the L2-torsion, the L2-torsion function, twisted L2-Euler characteristics and, in the case of a 3-manifold, the dual Thurston norm polytope.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MANIFOLDS; TORSION; INVARIANTS; NUMBERS; VOLUME; KNOTS; NORM; 57Q10 (primary); 57M27; 19B99 (secondary) |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Stefan Friedl |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:10 |
| Last Modified: | 12 Feb 2019 13:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/798 |
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