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Department of Mathematical Sciences

# Seminar Archives

## Pure Maths Colloquium: Rank gradient for groups and applications

Presented by Nikolay Nikolov, Imperial College London and Oxford

27 November 2006 16:00 in CM221

The \emph{rank gradient} $rg(G)$ of a finitely generated residually
finite group $G$ is a measure of the rate of growth of the number of
generators of subgroups of finite index in $G$. We relate this to the
invariant 'cost' of Levitt and Gaboriau of measure preserving ergodic
group actions. Using recent results by Golodets and Dooley and of Marc
Lackenby we disprove a conjecture about the Heegaard genus of
hyperbolic 3-manifolds.
This is joint work with Miklos Abert in Chicago.