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Epimorphisms between 2–bridge link groups

Tomotada Ohtsuki, Robert Riley and Makoto Sakuma

Geometry & Topology Monographs 14 (2008) 417–450

DOI: 10.2140/gtm.2008.14.417

arXiv: 0904.1856
Abstract

We give a systematic construction of epimorphisms between 2–bridge link groups. Moreover, we show that 2–bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2–bridge links and π1–dominating maps among 3–manifolds.

Dedicated to the memory of Professor Heiner Zieschang
Keywords

2-bridge knot, knot group, character variety, degree 1 map
Mathematical Subject Classification

Primary: 57M25

Secondary: 57M05, 57M50
References
Publication

Received: 30 May 2006
Revised: 15 March 2007
Accepted: 15 March 2007
Published: 29 April 2008
Authors
Tomotada Ohtsuki
Research Institute for Mathematical Sciences
Kyoto University
Sakyo-ku
Kyoto
606-8502
Japan
http://www.kurims.kyoto-u.ac.jp/~tomotada/
Robert Riley
Passed away on March 4, 2000
Makoto Sakuma
Department of Mathematics
Graduate School of Science
Hiroshima University
Higashi-Hiroshima
739-8526
Japan
http://www.math.sci.hiroshima-u.ac.jp/~sakuma/