Math 290, Spring 2011
Wednesday 10:40-12, 736 Evans
Organizer: Ian Agol
This semester, this seminar will focus on work of Dani Wise
and his collaborators on residual finiteness for hyperbolic
groups with a quasi-convex hierarchy. His results give a
proof of a conjecture of Baumslag that torsion one-relator groups
are residually finite. Another important consequence is that Haken
hyperbolic 3-manifolds are virtually fibered. We will spend a lot
of time discussing background material on one-relator groups,
hyperbolic groups, hierarchies, ends of groups and group pairs,
cube complexes, reflection groups and Artin groups,
subgroup separability, small cancellation theory,
and other geometric group theory concepts.
9/12: As Yi pointed out in lecture today, I mixed up the terms "Hopfian" and
The sketch of proof that BS(2,3) is non-Hopfian was correct, but I
incorrectly called it Hopfian.
Check out Henry Wilton's
blog, which has information about several topics we are covering
and Schupp, One relator groups and HNN extensions
Michah Sageev, Ends of group
pairs and Non-Positively Curved Cube Complexes
This paper (based on Sageev's UCB thesis) gives an equivalence
between an action of
a group G on a cube complex and a subgroup H<G such that the pair
(G,H) has more than one end.
This generalizes an equivalence between splittings of groups and
actions on trees.
Bergeron and Wise, A boundary criterion
and Wise, Special
This paper gives a criterion for a group to be a subgroup of a
right-angled Artin group, with
consequences for linearity and subgroup separability.
index subgroups of graph products
This paper generalizes Scott's separability argument to
word-quasiconvex subgroups of
abstract right-angled reflection groups.
Rita Gitik; Mahan Mitra; Eliyahu Rips; Michah Sageev, Widths of
This paper analyzes intersections of quasiconvex subgroups of a
Daniel Wise, The
residual finiteness of negatively curved polygons of finite groups
This paper considers the case of square complexes, which has some
simplifications over the case of
Haglund and Wise, A combination
theorem for special cube complexes
This paper is part of the inductive step for a group with a malnormal
Daniel Wise, The
structure of groups with a quasiconvex hierarchy
This gives a sketchy summary of Dani's results
Stefan Friedl, Notes
on a talk of Dani Wise
Notes by Friedl from the conference
in Montreal in April.
Hsu and Wise, Cubulating
graphs of free groups with cyclic edge groups
This paper shows how to obtain cubulations of amalgams. The
generalization of this technique is
needed for the inductive step.
virtual fibering conjecture and related questions, talk at the 2009
Georgia Topology conference