Graphs in locally 2-connected spaces

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• Carsten Thomassen (Technical University of Denmark)
• Thursday 29 May 2008, 14:30-15:30
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

It is well-known that the property of being locally connected simplifies the structure of a metric space considerably. Nevertheless, a complete description of the locally connected, compact metric spaces seems hopeless. However, a complete description becomes possible if we add the condition that the space does not contain an infinite complete graph and if we also strengthen the local connectivity condition to local 2-connectedness, that is, for every element x in the space, and every neighborhood U of x, there exists a neighborhood V of x contained in U such that both V and V-x are connected. Surprisingly, such a space must be locally 2-dimensional, that is, it is contained in a 2-dimensional surface. Some applications will be given.

This talk is part of the Combinatorics Seminar series.

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