[Binghamton Geometry/Topology Seminar] (no subject)

[Ross Geoghegan]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

          TWO SEMINARS THIS WEEK - SEPARATE ANNOUNCEMENTS FOR THE TWO

   Date: Tuesday (NOTE UNUSUAL DAY) April 10

   Time:  2.50 pm

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

   Speaker: Sarah Rees (University of Newcastle, England) 

   Title: Group geodesics: regularity, star-freedom and local testability 

         (This is joint with the Algebra Seminar.)


ABSTRACT: The geodesic words in a finitely generated group are known to
form a regular set whenever the group is either word hyperbolic or free
abelian. For selected generating sets, the same is true for virtually
abelian groups, geometrically finite hyperbolic groups, all Coxeter
groups, Artin groups of finite type and indeed all Garside groups;
this list does not claim to be exhaustive.

I report on an investigation to look for connections between algebraic
properties of such a group, combinatorial properties of its presentations,
the structure of its regular set of geodesics, and the complexity of
its word problem. That work is joint work with Gilman, Hermiller and Holt.

Terms such as regularity, star-freedom and local testability will be
defined in the talk; each can be shown to have several different disguises
(set-theoretic, geometric, or algebraic, in terms of an associated finite
semigroup). We shall see in particular that certain small cancellation
conditions on a presentation (which imply word hyperbolicity) force
the set of geodesic words to be star-free, that a rather restrictive
(but also natural) form of local testability of geodesics implies that
the word problem for that group is context-free, and hence characterises
virtually free groups, that 1-local testability characterises free abelian
groups, and that in general a group with locally testable geodesics can
have only finitely many conjugacy classes of torsion elements.



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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