[Binghamton Geometry/Topology Seminar] GEOMETRY/TOPOLOGY SEMINAR

[Tam Nguyen Phan]

   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


   Date: Thursday, September 18, 2014

   Time:  2.50 pm

   Place: Old Whitney Hall, Room 100E,  followed by coffee/tea in the
      Hilton Reading Room. Note the new location of the math department.


   Speaker: Russell Ricks (University of Michigan)

   Title: Flat strips in rank one CAT(0) spaces

Abstract:
Let X be a proper, geodesically complete CAT(0) space under a
geometric (that is, properly discontinuous, cocompact, and isometric)
group action on X; further assume X admits a rank one axis. Using the
Patterson-Sullivan measure on the boundary, we construct a generalized
Bowen-Margulis measure on the space of geodesics in X. This additional
structure allows us to prove some results about the original CAT(0)
space X. Here are three such results: First, with respect to the
Patterson-Sullivan measure, almost every point in the boundary of X is
isolated in the Tits metric. Second, under the Bowen-Margulis measure,
almost no geodesic bounds a flat strip of any positive width. Third,
we characterize when the length spectrum is arithmetic (that is, the
set of translation lengths is contained in a discrete subgroup of the
reals). In this talk, we will discuss the constructions and a few of the
wrinkles involved for CAT(0) spaces.


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

http://www2.math.binghamton.edu/p/seminars/topsem

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