Small 3-manifolds with large Heegaard distance

TL;DR

This paper constructs examples of closed hyperbolic 3-manifolds with Heegaard splittings of arbitrarily large distance, advancing understanding of the relationship between manifold topology and Heegaard complexity.

Contribution

It provides explicit constructions of non-Haken hyperbolic 3-manifolds exhibiting arbitrarily large Heegaard distance, a significant step in 3-manifold topology.

Findings

Existence of closed non-Haken hyperbolic 3-manifolds with large Heegaard distance

Explicit construction methods for such manifolds

Insights into the complexity of 3-manifold decompositions

Abstract

We construct examples of closed non-Haken hyperbolic 3-manifolds with a Heegaard splitting of arbitrarily large distance.