Genera and minors of multibranched surfaces

Shosaku Matsuzaki; Makoto Ozawa

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arXiv · 1603.09041

Genera and minors of multibranched surfaces

Shosaku Matsuzaki·Makoto Ozawa

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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, then we obtain a $1$-dimensional complex which is homeomorphic to a disjoint union of some $S^1$'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.

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Shosaku Matsuzaki, Makoto Ozawa. 2016-03-30. Genera and minors of multibranched surfaces. https://arxiv.org/abs/1603.09041

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