Manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings

TL;DR

This paper constructs infinitely many 3-manifolds that admit both strongly irreducible and weakly reducible minimal genus Heegaard splittings, expanding understanding of manifold decomposition structures.

Contribution

It introduces a method to construct infinitely many manifolds with both types of minimal genus Heegaard splittings, including closed and boundary-torus manifolds.

Findings

Existence of infinitely many such manifolds.

Construction of manifolds with both splitting types.

Applicability to closed and boundary-torus manifolds.

Abstract

We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.