Epimorphisms between 2–bridge link groups

2008/04/29 by Tomotada Ohtsuki, Robert Riley, Robert W. Riley +1 · 3 citations
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M05 #msc:57M25 #msc:57M50

paper · pdf · doi:10.2140/gtm.2008.14.417

published as Geom. Topol. Monogr. 14 (2008) 417-450 · This is the version published by Geometry & Topology Monographs on 29 April 2008

openalex publication_date 2008/04/29 · arxiv created 2009/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We give a systematic construction of epimorphisms between 2–bridge link groups. Moreover, we show that 2–bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2–bridge links and π1 –dominating maps among

Citations

• Non-zero degree maps between 2n-manifolds
• Markoff triples and quasifuchsian groups

Cited by

• Topological constraints on clean Lagrangian intersections via microlocal sheaf theory
• Presentation length and Simon's conjecture
• 1-domination of knots
• The SL(2,C) Casson invariant for Dehn surgeries on two-bridge knots

Related

• Epimorphisms from 2-bridge link groups onto Heckoid groups (II)
• Epimorphisms from 2-bridge link groups onto Heckoid groups (I)
• Genera of two-bridge knots and epimorphisms of their knot groups
• Generating function on epimorphisms between 2-bridge knot groups
• Parabolic generating pairs of genus-one 2-bridge knot groups