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Monthly Archives: May 2009
Groups with free subgroups
More ambitious than simply showing that a group is infinite is to show that it contains an infinite subgroup of a certain kind. One of the most important kinds of subgroup to study are free groups. Hence, one is interested … Continue reading
Posted in Groups
Tagged amenable groups, free groups, hyperbolic groups, laws, pingpong, Thompson's group, Tits alternative, von Neumann conjecture
3 Comments
Infinite groups
Before looking for surface subgroups, it is worth thinking about how to find (or rule out the existence of) simpler classes of subgroups. This is a very general question, and I do not intend to give a complete survey; however, … Continue reading
five week plan
As an experiment, I plan to spend the next five weeks documenting my current research on this blog. This research comprises several related projects, but most are concerned in one way or another with the general program of studying the … Continue reading
Posted in Overview
Tagged Gromov's question, hyperbolic groups, scl, stable commutator length, surface groups
4 Comments
The (strengthened) Hanna Neumann Conjecture
A few days ago, Joel Friedman posted a paper on the arXiv purporting to give a proof of the (strengthened) Hanna Neumann conjecture, a wellknown problem in geometric group theory. Simply stated, the problem is as follows. Conjecture (Hanna Neumann): … Continue reading →