Handlebody decompositions of three-manifolds and polycontinuous patterns. (27th April 2022)

• Record Type: Journal Article
• Authors: Sakata, N.; Mishina, R.; Ogawa, M.; Ishihara, K.; Koda, Y.; Ozawa, M.; Shimokawa, K.
• Is Part Of: Proceedings. Volume 478:Number 2260(2022)
• Publication Date: 2022-04-27
• Subjects: three-manifold -- handlebody decomposition -- polycontinuous pattern; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2022.0073
• Languages: English
• ISSNs: 1364-5021

Abstract

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.