To each finitely generated group is associated a sequence of non negative real numbers, its -Betti numbers. On the other hand, the set of finitely generated groups desingularizes into a usual topological space, the space MG of finitely generated marked groups. It is proved in this note that if a sequence of marked groups converges to a group , then .
Cite this article
Michael Pichot, Semi-continuity of the first <em><em>l</em><sup>2</sup></em>-Betti number on the space of finitely generated groups. Comment. Math. Helv. 81 (2006), no. 3, pp. 643–652DOI 10.4171/CMH/67