Monthly Archives: April 2011

Subgroups of products of surface and limit groups

This post is about strong generalizations of Baumslag and Roseblade’s theorem about subgroups of direct products of free groups. These generalizations were obtained by Bridson, Howie, Miller and Short. First they consider subgroups of direct products of surface groups. In … Continue reading

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Limit groups and residually free groups

The purpose of this post is to prepare for a discussion in our next post of three papers by Bridson, Howie, Miller and Short — the first about subgroups of direct products of surface groups, the second about subgroups of … Continue reading

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Surface subgroups of non-positively curved groups III: Right-angled Artin groups

This is the third of three posts based on a guest lecture by Sam Kim. In the last post, we considered the question of which Artin groups have hyperbolic surface subgroups. There we focused on Artin groups of finite and … Continue reading

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Surface subgroups of non-positively curved groups II: Artin groups

This is the second of three posts based on a guest lecture by Sam Kim. We now consider Gromov’s question about the existence of hyperbolic surface subgroups in the context of Artin groups — a family closely related to Coxeter … Continue reading

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Surface subgroups of non-positively curved groups I

This is the first of three posts based on a guest lecture by Sam Kim. In this post and the next we will consider the general question of which groups admit subgroups isomorphic to a surface group. We will focus … Continue reading

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A sketch of a proof of the Bestvina–Brady Theorem

In this post we will sketch a proof of the Bestvina–Brady Theorem. Let us first recall the definition of the Bestvina–Brady group, which was introduced in the last post. Consider a flag complex and its associated right–angled Artin group . … Continue reading

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Applications of the Bestvina-Brady Theorem

This post and the next will be mostly based on a 1996 paper by Mladen Bestvina and Noel Brady, Morse theory and finiteness properties of groups. Their main result (the Bestvina–Brady Theorem) relates topological properties of a flag complex to … Continue reading

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