Tag Archives: free groups

Faces of the scl norm ball

I am in Melbourne at the moment, in the middle of giving a lecture series, as part of the 2009 Clay-Mahler lectures (also see here). Yesterday I gave a lecture with the title “faces of the scl norm ball”, and … Continue reading

Posted in Dynamics, Groups, Surfaces | Tagged , , , , , , , , , | 1 Comment

scl, sails and surgery

I have just uploaded a paper to the arXiv, entitled “Scl, sails and surgery”. The paper discusses a connection between stable commutator length in free groups and the geometry of sails. This is an interesting example of what sometimes happens … Continue reading

Posted in Convex geometry, Groups | Tagged , , , , , , , , , | 1 Comment

van Kampen soup and thermodynamics of DNA

The development and scope of modern biology is often held out as a fantastic opportunity for mathematicians. The accumulation of vast amounts of biological data, and the development of new tools for the manipulation of biological organisms at microscopic levels … Continue reading

Posted in Biology, Dynamics, Groups | Tagged , , , , , , , | 4 Comments

Quasimorphisms and laws

A basic reference for the background to this post is my monograph. Let be a group, and let denote the commutator subgroup. Every element of can be expressed as a product of commutators; the commutator length of an element is the … Continue reading

Posted in Groups | Tagged , , , , | 3 Comments

Groups with free subgroups (part 2)

In a previous post, I discussed some methods for showing that a given group contains a (nonabelian) free subgroup. The methods were analytic and/or dynamical, and phrased in terms of the existence (or nonexistence) of certain functions on or on … Continue reading

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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 well-known problem in geometric group theory. Simply stated, the problem is as follows. Conjecture (Hanna Neumann): … Continue reading

Posted in Commentary, Groups | Tagged , , | 1 Comment

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 , , , , , , , | 3 Comments