[Binghamton Geometry/Topology Seminar] Geometry/Topology Seminar

[Christoforos Neofytidis]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

   Date: Thursday, February 16th, 2017

   Time: 2.50 pm

   Place: Whitney Hall, Room 100E

   Speaker: Tam Nguyen Phan (SUNY at Binghamton)

  Title: An analog of the Tits building in nonpositive curvature

Abstract: Locally symmetric manifolds (of noncompact type) form an
interesting class of nonpositively curved manifolds. By Borel-Serre, the
thin part of the universal cover of an arithmetic locally symmetric space
is homotopically equivalent to the  rational Tits building, which is
homotopically a wedge of spheres of dimension q-1, where Q is the Q-rank
of the locally symmetric space. In general, q is less than or equal to
n/2. We show that this is not an arithmetic coincidence in a weaker sense,
which is that if M is a noncompact, bounded nonpositively curved manifold
with finite volume and no arbitrarily small geodesic loops (so that M is
tame), then any nontrivial homology cycle in the thin part of \tilde{M}
must have dimension less than or equal to n/2 - 1. For each such cycle, we
construct a complex at infinity of dimension less than n/2 that is an
analog of the Tits building which we collapse the cycle onto. Simplices of
such a complex consist of points whose Busemann functions are invariant
under a group of parabolic isometries. You don't need to know what the
Tits building is but some familiarity with nonpositively curved geometry
will be helpful in understanding the talk.

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

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