OSU Mathematics Seminars and Colloquia
Wed, Feb 24, 2021
Topology Seminar
3:30 PM
Linking topology and combinatorics: Width-type parameters of 3-manifolds
Jonathan Spreer, University of Sydney
Host: Neil Hoffman
Contact Neil Hoffman for the seminar link. Also, for any Australians stopping by the talk is Thursday, 8:30AM AEDT.
[Abstract] [PDF]
Abstract: Many fundamental topological problems about 3-manifolds are algorithmically solvable in theory but continue to withstand practical computations. In recent years some of these problems have been shown to allow efficient solutions, if the input 3-manifold comes with a sufficiently "thin" presentation.

More specifically, a 3-manifold given as a triangulation is considered thin, if the treewidth of its dual graph is small. I will show how this combinatorial parameter, defined on a triangulation, can be linked back to purely topological properties of the underlying manifold. From this connection it can then be followed that, for some 3-manifolds, we cannot hope for a thin triangulation.

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