Refilling Meridians in a Genus 2 Handlebody Complement
نویسندگان
چکیده
Suppose a genus two handlebody is removed from a 3manifold M and then a single meridian of the handlebody is restored. The result is a knot or link complement in M and it is natural to ask whether geometric properties of the link complement say something about the meridian that was restored. Here we consider what the relation must be between two not necessarily disjoint meridians so that restoring each of them gives a trivial knot or a split link.
منابع مشابه
Comparing 2-handle Additions to a Genus 2 Boundary Component
A theorem concerning the effects of attaching a 2–handle to a suture on the boundary of a sutured manifold is used to compare the effects of two 2-handle attachments to a genus 2 boundary component of a compact, orientable 3–manifold. We obtain a collection of results relating the euler characteristic of a surface in one of the resulting 3– manifolds to the intersection number of the two curves...
متن کاملGenus Two Heegaard Spines in S 3
We study trivalent graphs in S3 whose closed complement is a genus two handlebody. We show that such a graph, when put in thin position, has a level edge connecting two vertices.
متن کاملA Simple Presentation of the Handlebody Group of Genus 2 Clement
For genus g = 2 I simplify Wajnryb’s presentation of the handlebody group.
متن کاملLayered - Triangulations of 3 – Manifolds
A family of one-vertex triangulations of the genus-g-handlebody, called layered-triangulations, is defined. These triangulations induce a one-vertex triangulation on the boundary of the handlebody, a genus g surface. Conversely, any one-vertex triangulation of a genus g surface can be placed on the boundary of the genus-g-handlebody in infinitely many distinct ways; it is shown that any of thes...
متن کاملSome Homological Invariants of Mapping Class Group of a 3-dimensional Handlebody
We show that, if g ≥ 2, the virtual cohomological dimension of the mapping class group of a 3-dimensional handlebody of genus g is equal to 4g − 5 and the Euler number of it is equal to 0.
متن کامل