## Algebraic & Geometric Topology

### Non-meridional epimorphisms of knot groups

#### Abstract

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.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 2 (2016), 1135-1155.

Dates
Revised: 1 June 2015
Accepted: 10 June 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841162

Digital Object Identifier
doi:10.2140/agt.2016.16.1135

Mathematical Reviews number (MathSciNet)
MR3493417

Zentralblatt MATH identifier
1345.57007

#### Citation

Cha, Jae Choon; Suzuki, Masaaki. Non-meridional epimorphisms of knot groups. Algebr. Geom. Topol. 16 (2016), no. 2, 1135--1155. doi:10.2140/agt.2016.16.1135. https://projecteuclid.org/euclid.agt/1510841162

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#### Supplemental materials

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