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1-Uryson width of surfaces

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NPCW06 - Non-positive curvature and applications

The $k$-Uryson width ($UW_k$) of a manifold gives a way to describe how close is the manifold to a $k$-dimensional complex. It turns out that this is a useful tool to approach several geometric problems.   In this talk I will give a brief survey of some applications of Uryson width and I will sketch the proof of the following two results:   1. If $\Sigma $ is a surface then $UW_1(\Sigma )\leq UW_1(\widetilde \Sigma)$.   2. If $M$ is a manifold with virtually cyclic fundamental group then $UW_1(M)\leq 6\cdot UW_1(\widetilde M)$.   (joint with H. Alpert, A. Banerjee )

This talk is part of the Isaac Newton Institute Seminar Series series.

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