Volume 14 (2008)

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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

Roots of torsion polynomials and dominations

Michel Boileau, Steve Boyer and Shicheng Wang

Geometry & Topology Monographs 14 (2008) 75–81

DOI: 10.2140/gtm.2008.14.75

arXiv: math.GT/0606703

Abstract

We show that the nonzero roots of the torsion polynomials associated to the infinite cyclic covers of a given compact, connected, orientable 3–manifold M are contained in a compact part of C* a priori determined by M. This result is applied to prove that when M is closed, it dominates at most finitely many Sol manifolds.

Dedicated to the memory of Heiner Zieschang

Keywords

nonzero degree map, torsion module, surface bundle, Sol manifold

Mathematical Subject Classification

Primary: 57M27

Secondary:

References
Publication

Received: 29 June 2006
Accepted: 5 February 2007
Published: 29 April 2008

Authors
Michel Boileau
Institut de Mathématiques de Toulouse, UMR 5219
Université Paul Sabatier
31062 Toulouse Cedex 9
France
Steve Boyer
Dépt de math
UQAM
PO Box 8888
Centre-ville, Montréal, Qc H3C 3P8
Canada
Shicheng Wang
LMAM
Department of Mathematics
Peking University
Beijing 100871
China