Hauptseminar Geometrie

Topological complexity (TC) was introduced by M. Farber as a numerical homotopy invariant motivated by the motion planning problem from robotics. It bears similarity with the Lusternik-Schnirelmann category. In this talk, I will present a result from joint work with Mark Grant in which we identify a topological condition on a symplectic manifold that ensures TC to coincide with a standard dimensional upper bound. This result is the TC analogue of a theorem by Rudyak-Oprea on the Lusternik-Schnirelmann category of symplectically aspherical manifolds. After an introduction to TC and the presentation of some basic results, I will explain how the cohomology groups of a space may be used to derive lower bounds on TC. I will then outline how these bounds are combined with infinite-dimensional de Rham theory to provide the abovementioned result for symplectic manifolds.

Montag, den 30. Juli 2018 um 10.00 Uhr, in Mathematikon, INF 205, SR A Montag, den 30. Juli 2018 at 10.00, in Mathematikon, INF 205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Benedetti