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

By Roberto Frigerio, Bruno Martelli, Carlo Petronio. 2002

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b2a492472afaec6bd9ef293f4e542289980278cd