Knot Group Epimorphisms, II
نویسنده
چکیده
We consider the relations ≥ and ≥p on the collection of all knots, where k ≥ k (respectively, k ≥p k) if there exists an epimorphism πk → πk of knot groups (respectively, preserving peripheral systems). When k is a torus knot, the relations coincide and k must also be a torus knot; we determine the knots k that can occur. If k is a 2-bridge knot and k ≥p k, then k is a 2-bridge knot with determinant a proper divisor of the determinant of k; only finitely many knots k are possible.
منابع مشابه
Knot Group Epimorphisms
Let G be a finitely generated group, and let λ ∈ G. If there exists a knot k such that πk = π1(S \k) can be mapped onto G sending the longitude to λ, then there exists infinitely many distinct prime knots with the property. Consequently, if πk is the group of any knot (possibly composite), then there exists an infinite number of prime knots k1, k2, · · · and epimorphisms · · · → πk2 → πk1 → πk ...
متن کاملNonsurjective epimorphisms in decomposable varieties of groups
A full characterization of when a subgroup H of a group G in a varietal product NQ is epimorphically embedded in G (in the variety NQ ) is given. From this, a result of S. McKay is derived , which states that if NQ has instances of nonsurjective epimorphisms, then N also has instances of nonsurjective epimorphisms. Two partial converses to McKay’s result are also given: when G is a finite nonab...
متن کاملErgodicity and Mixing of Noncommuting Epimorphisms
We study mixing properties of epimorphisms of a compact connected finite-dimensional abelian group X . In particular, we show that a set F , |F | > dimX , of epimorphisms of X is mixing iff every subset of F of cardinality (dimX)+1 is mixing. We also construct examples of free nonabelian groups of automorphisms of tori which are mixing, but not mixing of order 3, and show that, under some irred...
متن کاملFiniteness of 3-manifolds associated with non-zero degree mappings
We prove a finiteness result for the ∂-patterned guts decomposition of all 3manifolds obtained by splitting a given orientable, irreducible and ∂-irreducible 3manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a given compact 3-manifold belong, up to homeomorphism, to a finite collection of compact 3-manifo...
متن کاملOn semilattices of groups whose arrows are epimorphisms
A q partial group is defined to be a partial group, that is, a strong semilattice of groups S= [E(S);Se,φe, f ] such that S has an identity 1 and φ1,e is an epimorphism for all e ∈ E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1 = S1. This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended t...
متن کامل