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### Some metric properties of Thompson's group F

**Geometry/Topology**

Speaker: | Sean Cleary, City College of New York |

Location: | 693 Kerr |

Start time: | Thu, Jan 23 2003, 3:10PM |

Thompson's group F has a number of different manifestations- as a finitely-presented group, as an infinitely-presented group with a convenient set of normal forms, as a group of piecewise- linear homeomorphisms, and as a group of tree pair diagrams. Measuring the length of words in F via the tree pair diagram approach is possible using a remarkable process developed by Blake Fordham. `Dead-end words' are words whose word lengths are reduced when multiplied on the right by any generator or its inverse, and are `dead ends' in the sense that no geodesic ray from the identity in the Cayley graph can be continued beyond such words. We completely classify dead-end words in F which allows us to rule out previously-suspected more profound versions of dead-end phenomena in F. I will also discuss some other remarkable families of words in F, including some discovered during our proof that Thompson's group is not almost convex with respect to the standard generating set. This is joint work with Jennifer Taback.