Non-meridional epimorphisms of knot groups

Cha, Jae Choon¹ ; Suzuki, Masaaki²

¹Department 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
²Department of Frontier Media Science, Meiji University, 4–21–1 Nakano, Tokyo 164–8525, Japan

Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 1135-1155

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.1135

Classification : 20F34, 20J05, 57M05, 57M25
Keywords: knot groups, epimorphisms, meridians, twisted Alexander polynomials

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