## Quasi-isometries and the large scale geometry of infinite groups |

**Jennifer Taback**

November 1, 2000

3:45 - 4:45 pm

Bailey Hall 207

Refreshments in the common room at 3:30 pm

A quasi-isometry is a map between metric spaces which distorts distance by a bounded amount. One can view a finitely generated group G as a metric space using the word metric on the Cayley graph of G, and study quasi-isometries between infinite groups. I will define the large scale geometry of a group, and discuss which algebraic and combinatorial properties of this geometry are preserved under quasi-isometry. I will outline Gromov's program to classify all finitely generated groups up to quasi-isometry. I will state the four major classes of results on this program, focusing on my results for the groups PSL(2,Z[1/p]). These groups have a beautiful geometry which plays an important role in their quasi-isometry classification.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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