Topology Seminar
Fall 2013
Wednesday 11:10 am –
12 pm, Surge 268
October 2: Owen Baker, Intro to Gromov-hyperbolic groups
Abstract: This expository talk
assumes no background in geometric group theory. Geometric group theory studies
finitely generated groups in terms of geometric properties -- such as curvature
-- of the spaces they act on "geometrically". A group can act
geometrically on many different spaces, but these spaces are all
"quasi-isometric". Thus one desires combinatorial instead of
analytic notions of curvature. Being Gromov-hyperbolic (δ-hyperbolic) is quasi-isometry invariant, and can
sometimes be checked combinatorially. In this talk, I will talk about
several equivalent definitions of δ-hyperbolicity, and discuss
algorithmic consequences. Graduate students are invited to look through http://www.cmi.univ-mrs.fr/~hamish/Papers/MSRInotes2004.pdf.
October 9: Owen Baker, Cannon-Thurston maps do not always exist
Abstract: Associated to any
hyperbolic group is a topological space called its Gromov boundary.
Cannon and Thurston showed that if M is a hyperbolic 3-manifold fibering over
the circle S1 with fiber S, a hyperbolic surface, then the inclusion
of fundamental groups π1(S)->π1(M) induces a
map between their boundaries. Moreover, this map S1 ->S2
is a space-filling curve. We construct a hyperbolic group with a
hyperbolic subgroup for which inclusion does not induce a continuous map of the
boundaries. Joint with Tim Riley.
October 16: Julie Bergner, Partition complexes
October 23: Julie Bergner, Filtrations of Eilenberg Mac Lane spectra
October 30: Julie Bergner, Unitary partition complexes
November 6: No seminar
November 13: No seminar
November 20: Julie Bergner, Fixed points of the action of U(n) on L_n
November 27: Julie Bergner, Fixed points of the action of U(n) on L_n,
part 2
December 4: Bredon homology and partition complexes
http://www.math.ucr.edu/~jbergner/topologysem1314.htm Last
updated: 4 December 2013