| Résume | It is known by the Delorne-Guichardet theorem that, for $\sigma$-compact locally compact groups, property (T) coincides with property FH, that is the property that every continuous isometric action on a Hilbert space has a fixed point. Another rephrasing of this property is that for any unitary representation all $1$-cocycles have to be bounded. Inspired by the work of V.Lafforgue, for locally compact compactly generated groups, we explore the asymptotics of how unbounded can the 1-cocycles be in the case of a group without property FLp, an Lp-analogue of property FH. This is based on a joint work with Antonio López Neumann |
