2016/03/30 by Shosaku Matsuzaki, Makoto Ozawa, Matsuzaki, Shosaku +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1603.09041
openalex publication_date 2016/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We say that a 2-dimensional CW complex is a multibranched surface if we remove all points whose open neighborhoods are homeomorphic to the 2-dimensional Euclidean space, then we obtain a 1-dimensional complex which is homeomorphic to a disjoint union of some S1's. We define the genus of a multibranched surface X as the minimum number of genera of 3-dimensional manifold into which X can be embedded. We prove some inequalities which give upper bounds for the genus of a multibranched surface. A multibranched surface is a generalization of graphs. Therefore, we can define "minors" of multibranched surfaces analogously. We study various properties of the minors of multibranched surfaces.