The assessment for this course will be discussed with the students in class.
Course Description:
PART I: (before Spring Break)
This course will present some of the basic topics in geometric group theory, with a particular focus on coarse notions of curvature, such as delta-hyperbolic spaces and groups, but will also cover many other topics.
A student who has taken Math 547 (and maybe an undergraduate course in group theory) ought to have all of the prerequisites for this course.
PART II: (after Spring Break)
From Monday, March 26, I will begin to discuss Agol's (very) recent
proof of the Virtual Haken Conjecture.
The proof uses many techniques from geometric group theory, such as:
Special cube complexes, quasiconvex subgroups, subgroup separability,
relatively hyperbolic Dehn filling. It also relies on Wise's work on
special cube complexes and quasiconvex hierarchies (as well as some
of Wise's work with his collaborators, particularly Bergeron, Hsu and Haglund),
and on Kahn and Markovic's construction of (many) quasiconvex surface subgroups
in the fundamental groups of closed hyperbolic 3-manifolds. All of these aspects
will be discussed.
Reading for Part I:
Reading materials were discussed in class.
Reading for Part II:
For Wise's work, see:
here
(towards the bottom of the page, there is a `Manuscript', some `Lecture Notes', and a couple of other papers.)
Other references coming soon.
Instructor:
Daniel Groves groves@math.uic.edu
Office hours are TBA, or by appointment.
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