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Non-meridional
epimorphisms of knot groups
Jae Choon Cha and Masaaki Suzuki |
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Algebraic & Geometric Topology 16 (2016) 1135–1155
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Abstract |
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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 such that is a homomorphic image of but no epimorphism of onto preserves meridians. |
Keywords
knot groups, epimorphisms, meridians, twisted Alexander
polynomials
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Mathematical Subject Classification 2010
Primary: 20F34, 20J05, 57M05, 57M25
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Supplementary material |
References |
Publication
Received: 16 May 2015
Revised: 1 June 2015
Accepted: 10 June 2015
Published: 26 April 2016
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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 |
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