The rank of the fundamental group of certain hyperbolic 3-manifolds fibering over the circle

We determine the rank of the fundamental group of those hyperbolic 3-manifolds fibering over the circle whose monodromy is a sufficiently high power of a pseudo-Anosov map. Moreover, we show that any two generating sets with minimal cardinality are Nielsen equivalent.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200

Hyperbolic cone-manifolds with large cone-angles

We prove that every closed oriented 3-manifold admits a hyperbolic cone-manifold structure with cone-angle arbitrarily close to 2pi.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper24.abs.htm

On the Heegaard splittings of amalgamated 3-manifolds

We give a combinatorial proof of a theorem first proved by Souto which says the following. Let M_1 and M_2 be simple 3-manifolds with connected boundary of genus g>0. If M_1 and M_2 are glued via a complicated map, then every minimal Heegaard splitting of the resulting closed 3-manifold is an amalgamation. This proof also provides an algorithm to find a bound on the complexity of the gluing map.Comment: This is the version published by Geometry & Topology Monographs on 3 December 200

Requests of Brown by LC Classification: June 2005

Requests of Brown from other HELIN libraries - June 200

Checkouts by Institution: January 2006 HELIN /All Locations

Borrowing by institution - Juanuary 200