Semi-continuity of the first -Betti number on the space of finitely generated groups
Michael Pichot
École Normale Supérieure de Lyon, France
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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