Epimorphisms between 2-bridge link groups

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 pi_1-dominating maps among 3-manifolds.

This is the version published by Geometry & Topology Monographs on 29 April 2008

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Cited by in corpus (30)

• Epimorphisms and Boundary Slopes of 2-Bridge Knots
• A variation of McShane's identity for 2-bridge links
• Twisted Alexander polynomials and a partial order on the set of prime knots
• Epimorphisms between $2$-bridge knot groups and their crossing numbers
• Character varieties of double twist links
• Simon's conjecture for 2-bridge knots
• Twisted Alexander polynomials of 2-bridge knots associated to metacyclic representations
• The SL(2,C) Casson invariant for Dehn surgeries on two-bridge knots
• Twisted Alexander polynomials and character varieties of 2-bridge knot groups
• Classification of parabolic generating pairs of Kleinian groups with two parabolic generators
• Knot Group Epimorphisms, II
• A partial order on the set of prime knots with up to 11 crossings
• Presentation length and Simon's conjecture
• (t,s)-racks and their link invariants
• Tangle sums and factorization of A-polynomials
• Non-meridional epimorphisms of knot groups
• Some families of minimal elements for the partial ordering on prime knots
• Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions
• 1-domination of knots
• Simple loops on 2-bridge spheres in 2-bridge link complements
• Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
• On standard forms of 1--dominations between knots with same Gromov volumes
• A new proof for small cancellation conditions of 2-bridge link groups
• Genera of two-bridge knots and epimorphisms of their knot groups
• Symplectic quandles and parabolic representations of 2-bridge Knots and Links
• Torsion in Kauffman bracket skein module of a $4$-strand Montesinos knot exterior
• Generating function on epimorphisms between $2$-bridge knot groups
• Overcommuting pairs in groups and 3-manifolds bounding them
• Parabolic generating pairs of genus-one 2-bridge knot groups
• Simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links