Algebraic & Geometric Topology

Non-meridional epimorphisms of knot groups

Jae Choon Cha and Masaaki Suzuki

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx] 20J05: Homological methods in group theory 57M05: Fundamental group, presentations, free differential calculus 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

knot groups epimorphisms meridians twisted Alexander polynomials


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.

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Supplemental materials

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