Sakata N, Mishina R, Ogawa M, Ishihara K, Koda Y, Ozawa M, Shimokawa K
Department of Mathematics, Saitama University, Saitama 338-8570, Japan.
Faculty of Education, Yamaguchi University, Yamaguchi 753-8511, Japan.
Proc Math Phys Eng Sci. 2022 Apr;478(2260):20220073. doi: 10.1098/rspa.2022.0073. Epub 2022 Apr 20.
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.
我们引入三维流形的柄体分解概念，它是希盖尔分裂或三分法的一种推广。我们证明了闭可定向三维流形的两个柄体分解是稳定等价的。作为对材料科学的应用，我们考虑多连续模式的数学模型，并讨论嵌段共聚物熔体微相分离的拓扑研究。
