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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.