#### 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.

Done