Geometry and analysis of groups and manifolds

The isoperimetric rank of a Carnot group

speaker: Fedya Manin

abstract: To what extent can the geometry of a Carnot group be read off from its algebraic properties? From the point of view of filling functions (that is, how hard it is to fill n-dimensional holes, in any of a number of senses) Carnot groups exhibit Euclidean behavior up to a critical dimension in which filling is harder than in Euclidean space. For step 2 Carnot groups, Gromov gave a (not always sharp) lower bound for this critical dimension. We give a cohomological upper bound which is sharp seemingly in all known cases. For certain examples (e.g. octonionic Heisenberg groups and Wenger's groups with non-strictly polynomial Dehn function) this leads to a new lower bound on Lipschitz filling functions. This is work in progress, some of it with Robert Young.

timetable:
Thu 29 Jun, 15:00 - 15:30, Aula Dini
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