Iain R. Aitchison

Learn More
Given a hyperbolic 3{manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M . As a corollary, we show that the smallest volume orientable hyperbolic 3{manifold has volume > :32. AMS Classi cation numbers Primary: 57M50 Secondary: 53C15, 53C22
We prove that for any free group automorphism +* having a specified form there exists an invertible ribbon disc pair (B4,D2) such that the closure of B4 nbd(D2) fibres over the circle with fibre a handlebody and monodromy equal to X*. We apply this to obtain results about ribbon 1and 2-knots. 0. Introduction and preliminaries. This paper is motivated by the(More)
We associate to each finite presentation of a group G a compact CWcomplex that is a 3-manifold in the complement of a point, and whose fundamental group is isomorphic to G. We use this complex to define a notion of genus for G and give examples, and also define a notion of ‘closed group’. A group has genus 0 if and only if it is the fundamental group of a(More)
A combinatorial condition is obtained for when immersed or embedded incompressible surfaces in compact 3–manifolds with tori boundary components remain incompressible after Dehn surgery. A combinatorial characterisation of hierarchies is described. A new proof is given of the topological rigidity theorem of Hass and Scott for 3–manifolds containing immersed(More)
It is known that about 70% of surgeries on the figure 8 knot give manifolds which contain immersed incompressible surfaces. We improve this to about 80% by giving a very simple proof that all even surgeries give manifolds containing such a surface. Moreover, we give a quick proof that every (6k, t) surgery is virtually Haken, thereby partially dealing with(More)