Hall 123

Topological rank and cost

Francois Le Maitre

University of Paris VII

The topological rank of a topological group is the minimum
number of elements needed to generate a dense subgroup. For instance,
it is a nice exercise to show that the topological rank of R^n is n+1:
in other words the topological rank of a finite dimensional real
vector space is equal to its dimension plus one. In this talk, I will
explain a similar formula relating the cost of a measure preserving
ergodic equivalence relation and the topological rank of its full group.