Non-meridional epimorphisms of knot groups

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.

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Keywords

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 $J_{-1}$

References

Publication

Received: 16 May 2015

Revised: 1 June 2015

Accepted: 10 June 2015

Published: 26 April 2016

Authors

Jae Choon Cha
Department of Mathematics Pohang University of Science and Technology Gyeongbuk 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 Japan

Volume 16, issue 2 (2016)

Jae Choon Cha and Masaaki Suzuki

Abstract