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DIMAP Seminar: Johannes Carmesin (University of Birmingham)

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Location: D1.07

Embedding simply connected 2-complexes in 3-space.

A classical theorem of Kuratowski characterises graphs embeddable in the plane by two obstructions. More precisely, a graph is planar if and only if it does not contain the complete graph K_5 or the complete bipartite graph K_{3,3} as a minor.

Can you characterise embeddability of 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski鈥檚 characterisation of graph planarity?

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