Complexity and Heegaard genus of an infinite class of compact 3-manifolds

Roberto Frigerio, Bruno Martelli and Carlo Petronio

Vol. 210 (2003), No. 2, 283–297

DOI: 10.2140/pjm.2003.210.283

Abstract

Using the theory of hyperbolic manifolds with totally geodesic boundary, we provide for every n ≥ 2 a class ℳ_n of such manifolds all having Matveev complexity equal to n and Heegaard genus equal to n + 1. All the elements of ℳ_n have a single boundary component of genus n, and #ℳ_n grows at least exponentially with n.

Milestones

Received: 3 July 2002

Revised: 14 September 2002

Published: 1 June 2003