Handlebody decompositions of 3-manifolds and polycontinuous patterns

Naoki Sakata; Ryosuke Mishina; Masaki Ogawa; Kai Ishihara; Yuya Koda; Makoto Ozawa; Koya Shimokawa

doi:10.1098/rspa.2022.0073

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arXiv · 2201.11420

Handlebody decompositions of 3-manifolds and polycontinuous patterns

Naoki Sakata·Ryosuke Mishina·Masaki Ogawa·Kai Ishihara·Yuya Koda·Makoto Ozawa·Koya Shimokawa

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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.

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Naoki Sakata, Ryosuke Mishina, Masaki Ogawa, Kai Ishihara, Yuya Koda, Makoto Ozawa, Koya Shimokawa. 2022-01-27. Handlebody decompositions of 3-manifolds and polycontinuous patterns. https://doi.org/10.1098/rspa.2022.0073

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