Epimorphism sequences between hyperbolic 3-manifold groups

Abstract

Abstract. We will show that any infinite sequence of epimorphisms between finitely generated hyperbolic 3-manifold groups eventually consists of isomorphisms.In this paper, we are interested in sequences M 0

Epimorphisms between 2–bridge link groups

“…Thus the problem of epimorphisms between knot groups is related to the study of proper maps between ambient spaces, more generally, maps between 3-manifolds. This direction has been extensively studied in various literatures (see Boileau-Wang [3], Boileau-Rubinstein-Wang [4], Kawauchi [20], Reid-Wang-Zhou [31], Silver-Whitten [40], Soma [41,42], Wang [43] and references therein).…”

“…Then for every manifold M(s) (s ∈Q), obtained by s-surgery on K(r), the map f : We present yet another application of Theorem 1.2 to π 1 -surjective maps. By studying the character varieties, Soma [42] observed that there is no infinite descending tower of π 1 -surjective maps between orientable hyperbolic 3-manifolds, namely, any infinite sequence of π 1 -surjective maps…”

Epimorphisms between 2-bridge link groups: homotopically trivial simple loops on 2-bridge spheres

“…Moreover we have a partial order on the set of prime knots, by setting K ≥ K if there is an epimorphism G( K) → G(K) (see, for example, [32,Proposition 3.2]). Epimorphisms among link groups have received considerable attention and they have been studied in various places in the literature (see [1,2,5,6,10,11,15,16,17,25,27,30,32,33,34,35,36] and references therein).…”

Hyperbolic 3-manifolds of low cusp volume

“…If φ : π 1 → Γ is an epimorphism, then it is an isomorphism. Proof We adapt and closely follow an argument of [Som02]. Since H 3 /Γ is a cusped finite-volume hyperbolic 3-manifold, we can lift Γ to SL(2, C) as Γ.…”