Fateme Yegane Mokari (São Paulo/UCD)

will speak on

Virtual rational Betti numbers of soluble groups of homological type $FP_n$

Time: 2:00PM
Date: Thu 7th November 2019
Location: Seminar Room SCN 1.25 [map]

Further information

Abstract: The virtual rational Betti numbers of a finitely generated group studies the growth of Betti numbers of the group as one follows passage to subgroups of finite index. More precisely, the n-th virtual rational Betti number of a finitely generated group G is defined as

$vb_n(G):=\sup_{M \in A_G} \mbox{dim } H_n(M, Q)$,

where $A_G$ is the set of all subgroups of finite index in $G$. In this talk we will discuss the virtual rational Betti numbers of nilpotent-by-abelian groups that satisfy certain finiteness condition. Note that a group $G$ is called nilpotent-by-abelian if $G$ has a nilpotent normal subgroup $N$ such that $G/N$ is abelian. These groups are solvable.

(This talk is part of the Algebra and Number Theory series.)

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