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Geometry and analysis of groups and manifolds

Embeddings of Nilpotent groups into L1

speaker: Sebastiano Nicolussi Golo (Jyväskylän Yliopisto)

abstract: We shall present the proof that virtually abelian groups are the only nilpotent Lie groups that quasi-isometrically embed in the Banach space L¹ of integrable functions. From an asymptotic-cone argument we shall reduce to the case of bi-Lipschitz embeddings of Carnot groups. Cheeger and Kleiner proved that Heisenberg groups do not embed in L¹ spaces: we shall extend their result to all non-abelian Carnot groups, by overcoming a difficulty due to the structure of finite-perimeter sets and their blowups. From a collaboration with S. Eriksson-Bique, C. Gartland, E. Le Donne and L. Naples.

timetable:
Mon 26 Jun, 15:00 - 15:30, Aula Dini
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