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Embeddings of multibranched surfaces into 3-manifolds

Ponente: Makoto Ozawa
Institución: Komazawa University
Tipo de Evento: Investigación
Cuándo 23/02/2017
de 13:00 a 14:30
Dónde Salon de Seminarios Graciela Salicrup
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(partially joint work with Kazufumi Eto, Shosaku Matsuzaki, Mario
Eudave-Munoz)

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.