Semi-continuity of the first -Betti number on the space of finitely generated groups

  • Michael Pichot

    École Normale Supérieure de Lyon, France

Abstract

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 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 -Betti number on the space of finitely generated groups. Comment. Math. Helv. 81 (2006), no. 3, pp. 643–652

DOI 10.4171/CMH/67