Volume 16, issue 2 (2016)

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Non-meridional epimorphisms of knot groups

Jae Choon Cha and Masaaki Suzuki

Algebraic & Geometric Topology 16 (2016) 1135–1155

In the study of knot group epimorphisms, the existence of an epimorphism between two given knot groups is mostly (if not always) shown by giving an epimorphism which preserves meridians. A natural question arises: is there an epimorphism preserving meridians whenever a knot group is a homomorphic image of another? We answer in the negative by presenting infinitely many pairs of prime knot groups (G,G) such that G is a homomorphic image of G but no epimorphism of G onto G preserves meridians.

knot groups, epimorphisms, meridians, twisted Alexander polynomials
Mathematical Subject Classification 2010
Primary: 20F34, 20J05, 57M05, 57M25
Supplementary material

Table of twisted Alexander polynomials of the knot $J_{-1}$

Received: 16 May 2015
Revised: 1 June 2015
Accepted: 10 June 2015
Published: 26 April 2016
Jae Choon Cha
Department of Mathematics
Pohang University of Science and Technology
Pohang 790-784
South Korea
School of Mathematics
Korea Institute for Advanced Study
Seoul 130–722
South Korea
Masaaki Suzuki
Department of Frontier Media Science
Meiji University
4–21–1 Nakano
Tokyo 164–8525