T. Schick: L²-Betti numbers and a conjecture of Gottlieb
A classical result of Gottlieb established that the Euler characteristic of a group is zero, provided it contains a normal subgroup isomorphic to Z. Recently, he conjectured similar properties of mapping degrees of maps between classifying spaces (these mapping degrees suitably defined). As originally stated, this conjecture is wrong. The theorem of Gottlieb has been vastly generalized (and the proof simplified) using L²-Betti numbers. We will use L²-Betti number techniques to establish the correct theorem about mapping degrees (again in a more general context than proposed by Gottlieb). Along the way, we will introduce the main results and definitions about L²-Betti numbers.