[Topology.beta] AG Tomorrow.

[Rot, T.O. (Thomas)]

Happning in 5!

From: "Rot, T.O. (Thomas)" <t.o.rot at vu.nl>
Date: Monday, 25 March 2024 at 16:44
To: "_list_topology.beta" <topology.beta at listserver.vu.nl>
Subject: AG Tomorrow.

Dear all,

Fabio will not speak about his life, but he will speak about

Cellular embeddings of levelled spatial graphs
Abstract: Every abstract graph can be embedded on a closed oriented surface and the genus range for the surface is known. If, instead of an abstract graph, an embedding of a graph is considered, it is still easy to find a closed oriented surface on which the spatial graph is embedded on by placing the graph on the boundary of a tubular neighbourhood of the graph. But in general there is no good control over the complement of the graph in a surface, it could be a union of discs with any number of punctures. We are interested in finding surfaces for a spatial graph, such that the complement of the graph in the surface is a set of open discs, so called cellular embeddings. To this end, we introduce a new family of spatial graphs, called levelled embeddings. The defining feature of levelled embeddings is their decomposition into planar subgraphs, all of which are interconnected through a common cycle within the graph. This structure allows for a systematic exploration of their embedding possibilities. We prove that levelled embeddings of low complexity can always be cellular embedded. We extend this result in a sufficient condition for finding cellular embeddings of levelled graphs with arbitrarily high complexity.

Party starts at 11:00 in Maryam.

See you there!
Thomas
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