Sakata N, Mishina R, Ogawa M, Ishihara K, Koda Y, Ozawa M, Shimokawa K. Handlebody decompositions of three-manifolds and polycontinuous patterns.
Proc Math Phys Eng Sci 2022;
478:20220073. [PMID:
35510221 PMCID:
PMC9053369 DOI:
10.1098/rspa.2022.0073]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Accepted: 03/10/2022] [Indexed: 11/12/2022] Open
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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