An afternoon on asymptotic dimension

Abstract: 15.00 - 15.45 Panos Papazoglu (Oxford)

16.00 - 16.45 Urs Lang (ETH Zurich)

17.15 - 18.00 Karim Adiprasito (Hebrew University & University of Copenhagen)

Panos Papazoglu, "Asymptotic dimension of planes" (joint with K. Fujiwara)

It is easy to see that there are Riemannian manifolds homeomorphic to $\mathbb R ^3$ with infinite asymptotic dimension. In contrast to this we showed with K. Fujiwara that the asymptotic dimension of Riemannian planes (and planar graphs) is bounded by 3. This was improved to 2 by Jorgensen-Lang and Bonamy-Bousquet-Esperet-Groenland-Pirot-Scott.

Urs Lang, "Assouad-Nagata dimension and Lipschitz extensions "

It follows from a recent result of Fujiwara-Papasoglu and a Hurewicz-type theorem due to Brodskiy-Dydak-Levin-Mitra that every planar geodesic metric space has

(Assouad-)Nagata dimension at most two and hence asymptotic dimension at most two. This can be used further to prove that every three-dimensional Hadamard manifold

has Nagata dimension three and is an absolute Lipschitz retract (joint work with Martina Jørgensen). The role of the Nagata dimension in Lipschitz extension problems will be discussed further.

Karim Adiprasito, "l^2 cohomology and stable Lefschetz theory"

group theorymetric geometry

Audience: researchers in the topic

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ENS group theory seminar

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