Tag Archives: surface groups

Surface subgroups – more details from Jeremy Kahn

Jeremy Kahn kindly sent me a more detailed overview of his argument with Vlad Markovic, that I blogged earlier about here (also see Jesse Johnson’s blog for other commentary). With his permission, this is reproduced below in its entirety. Editorial … Continue reading

Posted in 3-manifolds, Ergodic Theory, Surfaces | Tagged , , , | 4 Comments

Surface subgroups in hyperbolic 3-manifolds

I just learned from Jesse Johnson’s blog that Vlad Markovic and Jeremy Kahn have announced a proof of the surface subgroup conjecture, that every complete hyperbolic -manifold contains a closed -injective surface. Equivalently, contains a closed surface subgroup. Apparently, Jeremy … Continue reading

Posted in 3-manifolds, Ergodic Theory, Surfaces | Tagged , , , , , , , , | 10 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

Posted in Groups | Tagged , , , , , , , , | Leave a comment

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 , , , , | 4 Comments