L2-torsion invariants of a surface bundle over S1

Teruaki Kitano; Takayuki Morifuji; Mitsuhiko Takasawa

doi:10.2969/jmsj/1191418642

L²-torsion invariants of a surface bundle over S¹

Teruaki Kitano, Takayuki Morifuji, Mitsuhiko Takasawa

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In the present paper, we introduce L²-torsion invariants τ_k(k ≥ 1) for surface bundles over the circle and investigate them from the view point of the mapping class group of a surface. It is conjectured that they converge to the L²-torsion for the regular representation of the fundamental group. Further we give an explicit and computable formula of the first two invariants by using the Mahler measure.

Original language	English
Pages (from-to)	503-518
Number of pages	16
Journal	Journal of the Mathematical Society of Japan
Volume	56
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/1191418642
Publication status	Published - 2004
Externally published	Yes

Keywords

Hyperbolic volume
L-torsion
Nilpotent quotient
Surface bundle

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/1191418642

Cite this

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AU - Kitano, Teruaki

AU - Morifuji, Takayuki

AU - Takasawa, Mitsuhiko

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AB - In the present paper, we introduce L2-torsion invariants τk(k ≥ 1) for surface bundles over the circle and investigate them from the view point of the mapping class group of a surface. It is conjectured that they converge to the L2-torsion for the regular representation of the fundamental group. Further we give an explicit and computable formula of the first two invariants by using the Mahler measure.

KW - Hyperbolic volume

KW - L-torsion

KW - Nilpotent quotient

KW - Surface bundle

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