| Time: | 12 - 1:30 p.m. |
| Room: |
Wean Hall 7220
|
| Speaker: | Paul Gartside Assistant Professor Department of Mathematics University of Pittsburgh |
| Title: |
Polish groups strive for freedom, but never make it ...
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| Abstract: |
First we consider the problem of when a Polish topological group is
`almost free' in the sense that randomly chosen elements of the group
generate a free subgroup, and when a Polish group has a dense free
subgroup. Applications are given to automorphism groups of first order
structures and other Polish groups. (Joint work with Robin Knight.)
Then we turn to the question of whether a Polish group can itself be a free group. Except in the trivial case of a countable free group with the discrete topology the answer is `no'. This last result was independently proved by Shelah. |