Handlebody decompositions of three-manifolds and polycontinuous patterns

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

doi:10.1098/rspa.2022.0073

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 journal › Article › peer-review

Abstract

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 language	English
Article number	20220073
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	478
Issue number	2260
DOIs	https://doi.org/10.1098/rspa.2022.0073
Publication status	Published - 2022
Externally published	Yes

Keywords

handlebody decomposition
polycontinuous pattern
Three-manifold

ASJC Scopus subject areas

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

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10.1098/rspa.2022.0073

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title = "Handlebody decompositions of three-manifolds and polycontinuous patterns",

abstract = "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.",

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author = "N. Sakata and R. Mishina and M. Ogawa and K. Ishihara and Y. Koda and M. Ozawa and K. Shimokawa",

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language = "English",

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T1 - Handlebody decompositions of three-manifolds and polycontinuous patterns

AU - Sakata, N.

AU - Mishina, R.

AU - Ogawa, M.

AU - Ishihara, K.

AU - Koda, Y.

AU - Ozawa, M.

AU - Shimokawa, K.

N1 - Funding Information: This research is supported by MEXT Grants-in-Aid for Scientific Research on Innovative Areas (JP17H06460 and JP17H06463) and JSPS KAKENHI grant no. JP21H00978. Acknowledgements Publisher Copyright: © 2022 The Author(s).

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

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KW - polycontinuous pattern

KW - Three-manifold

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Handlebody decompositions of three-manifolds and polycontinuous patterns

Abstract

Keywords

ASJC Scopus subject areas

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