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Free groups and actions on trees
Student-Run Geometry/Topology| Speaker: | Yvonne Lai, UC Davis |
| Location: | 693 Kerr |
| Start time: | Thu, Nov 10 2005, 12:40PM |
Description
In the 1920's, Nielsen and Schreier proved that every subgroup of
a free group is free. This theorem is a corollary of the fact
that a group is free if and only if it acts freely on a tree.
Using discussion of this theorem (and its proof) as a starting
point, we will discuss a generalization of this statement
(Karass-Pietreski-Solitar) and its consequences for the study
of the outer automorphism group Out(F_n) of the free group.
Time permitting, we will state (without proof) some facts
about Outer Space, an interesting space that Out(F_n) acts on.