Simplical structures of knot complements

Simplicial Structures of Knot Complements

It was shown in [5] that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot complements. The explicit formula for the bound is in terms of the numbers of tetrahedr...

Braid structures in knot complements , handlebodies and 3 – manifolds Sofia

We consider braids on m + n strands, such that the first m strands are trivially fixed. We denote the set of all such braids by Bm,n. Via concatenation Bm,n acquires a group structure. The objective of this paper is to find a presentation for Bm,n using the structure of its corresponding pure braid subgroup, Pm,n, and the fact that it is a subgroup of the classical Artin group Bm+n. Then we giv...

Geometric Limits of Knot Complements

We prove that any complete hyperbolic 3–manifold with finitely generated fundamental group, with a single topological end, and which embeds into S is the geometric limit of a sequence of hyperbolic knot complements in S. In particular, we derive the existence of hyperbolic knot complements which contain balls of arbitrarily large radius. We also show that a complete hyperbolic 3–manifold with t...

Geodesic Surfaces in Knot Complements

Floer Homology and Knot Complements

We use the Ozsváth-Szabó theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call ĈF r. It carries information about the Ozsváth-Szabó Floer homology of large integral surgeries on the knot. Using the exact triangle, we derive information about other surgeries on knots, and about the maps on ...