Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777799 | Topology and its Applications | 2017 | 18 Pages |
Abstract
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 R2, 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Shosaku Matsuzaki, Makoto Ozawa,