[Binghamton Geometry/Topology Seminar] (no subject)

[Ross Geoghegan]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


   Date: Thursday February 23, 2006 

   Time:  2.50 pm

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

   Speaker: Mike Mihalik (Vanderbilt) 

   Title: Decompositions of Coxeter Groups over minimal splittings 

ABSTRACT:
(Joint work with Steve Tschantz) The first "accessibility" questions for
finitely generated groups arose from Stallings' splitting theorem for
infinite ended groups. Later Dunwoody proved that finitely presented
groups are indeed accessible with respect to splittings over finite
groups. Bestvina and Feighn followed Dunwoody's result with an
accessibility result for finitely presented groups when splitting
subgroups are "small." The notion of JSJ-decompositions of finitely
presented groups arose from geometrical/algebraic decompositions
of closed 3-manifolds over certain embedded separating surfaces. For
1-ended finitely presented groups Rips and Sela showed the existence of
(unique) JSJ decompositions over 2-ended splittings. Dunwoody and Sageev
introduced the notion of minimal virtually abelian splitting subgroups
into the JSJ arena. We introduce a notion of "strong accessibility" over
minimal splittings of groups that naturally generalizes the original
accessibility results over finite and small splitting subgroups. We
discuss two results. The first is a strong accessibility result for
finitely generated Coxeter groups over minimal splittings. The second is
a "best possible" JSJ-result for splitting finitely generated Coxeter
groups over virtually abelian splitting subgroups. Splittings over
minimal virtually abelian subgroups plays an important role in the
JSJ result. Both results are "visual" in the sense that the critical
decompositions involved can be "seen" geometrically in the presentation
diagram of a Coxeter group.

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.
_____________________
IF YOU WANT TO BE REMOVED FROM THIS EMAIL LIST WRITE
ross at math.binghamton.edu