On Tuesday, Şükrü gave a talk in our groups and combinatorics seminar on material related to last week’s discussion. The slides of his talk are available on our seminars page and include a definition of a Phan system.

Alice Devillers led the discussion in the study group on Friday to give a buildings perspective on last week’s discussion by Şükrü.

Recall that a chamber system consists of a set of chambers such that two chambers are -adjacent if they agree in all but their elements of type . See also this earlier discussion. We say that a chamber system is *simply 2-connected* if every closed path can be reduced to the trivial path bya sequence replacing any subpath lying in a rank 2 residue by another path in the same residue, that is, any closed path is *2-homotopy equivalent* to the trivial path. Buildings are simply 2-connected chamber systems.

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