[Binghamton Geometry/Topology Seminar] (no subject)

[Ross Geoghegan]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


   Date: Thursday October 27, 2005 

   Time:  2.50 pm

   Place: Library North 2205 followed by coffee/tea in the Anderson
          Reading Room.

   Speaker: Tim Riley (Cornell)

   Title: Intrinsic versus extrinsic diameter in finitely presented groups

Abstract: 

I will explain recent work with Martin Bridson on the diameter and
filling length of van Kampen diagrams in finitely presented groups.
There are two natural ways to measure the diameter of a combinatorial
disc D (a van Kampen diagram) mapped into the Cayley 2-complex of a
finitely presented group: either intrinsically, using the path metric
on the 1-skeleton of D, or extrinsically, using the path metric on the
Cayley graph (the word metric). One expects intrinsic diameter to be
qualitatively larger than extrinsic diameter in general. I will give
groups that confirm this intuition.  The constructions involved also speak
to issues concerning filling length, a filling invariant that controls
the length of the contracting curve in the course of a null-homotopy
of a loop in a Cayley 2-complex. I will exhibit a group in which the
filling lengths of loops vary dramatically depending on whether or not
one keeps a base vertex fixed during the null-homotopy.


NOTE:  The seminar has a webpage where the semester's program is listed:

http://math.binghamton.edu/MATH/dept/topsem/index.html

It can also be linked from the Department's Home Page.
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