Handlebody decompositions of 3-manifolds and polycontinuous patterns

TL;DR

This paper introduces handlebody decompositions for 3-manifolds, proves their stable equivalence, and applies this topological framework to model and analyze microphase separation in polycontinuous patterns within materials science.

Contribution

It generalizes existing 3-manifold decompositions and applies topological methods to study complex patterns in block copolymer melts.

Findings

Handlebody decompositions are stably equivalent for closed orientable 3-manifolds.

Topological modeling provides insights into microphase separation.

Application to materials science demonstrates practical relevance.

Abstract

We introduce the concept of a handlebody decomposition of a 3-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a closed orientable 3-manifold are stably equivalent. As an application to materials science, we consider a mathematical model of polycontinuous patterns and discuss a topological study of microphase separation of a block copolymer melt.