## Topology & Geometric Group Theory Seminar

## Spring 2010

### 1:30 – 2:30, Malott 203

Tuesday, February 9

**Jason
Manning**, University at Buffalo

*Virtually geometric words and Whitehead's algorithm*

Whitehead's algorithm takes a collection of (cyclic) words in a free
group and reduces them to minimal length. Results of Berge and
Zieschang relate the tools used in Whitehead's algorithm to the
realizability problem for Heegaard splittings. (This is the question
of which finite group presentations are presentations for fundamental
groups of 3-manifolds of a special form which comes from a Heegaard
diagram.) It turns out these ideas are also applicable to a recent
question of Gordon and Wilton about whether every presentation with a
single relator is "virtually geometric"—this is related in turn
to the question of which hyperbolic groups contain surface subgroups.
I'll discuss some of these ideas and answer Gordon and Wilton's
question.

Back to seminar home page.