Friedl, Stefan and Lueck, Wolfgang (2019) The L-2-torsion function and the Thurston norm of 3-manifolds. COMMENTARII MATHEMATICI HELVETICI, 94 (1). pp. 21-52. ISSN 0010-2571, 1420-8946
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Let M be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary which is not S(1)x D-2. Consider any element phi in the first cohomology of M with integer coefficients. Then one can define the phi-twisted L-2-torsion function of the universal covering which is a function from the set of positive real numbers to the set of real numbers. By earlier work of the second author and Schick the evaluation at t = 1 determines the volume. In this paper we show that the degree of the L-2-torsion function, which is a number extracted from its asymptotic behavior at 0 and at infinity, agrees with the Thurston norm of phi.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | L-2-ALEXANDER INVARIANT; TORSION; MANIFOLDS; L-2-INVARIANTS; APPROXIMATION; L(2)-TORSION; L-2-Betti numbers; L-2-torsion; twisting with finite-dimensional representations; Thurston norm |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Stefan Friedl |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Apr 2020 11:35 |
| Last Modified: | 27 Apr 2020 11:35 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27847 |
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