Handlebody decompositions of three-manifolds and polycontinuous patterns

N. Sakata, R. Mishina, M. Ogawa, K. Ishihara, Y. Koda, M. Ozawa, K. Shimokawa

Research output: Contribution to journalArticlepeer-review


We introduce the concept of a handlebody decomposition of a three-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a closed orientable three-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.

Original languageEnglish
Article number20220073
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2260
Publication statusPublished - 2022
Externally publishedYes


  • handlebody decomposition
  • polycontinuous pattern
  • Three-manifold

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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