Mark Hagen (Bristol) - Guirardel cores for cube complexes
на канале: 2017-2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions
Graphs, surfaces, and cube complexes
10 July 2018
Abstract: Given a group G acting on two simplicial trees T1,T2, the Guirardel core is a G--invariant subcomplex of T1×T2 that records how "compatible" the two splittings of G are, and allows one to sensibly define an intersection number for the two splittings. It turns out that, generalising Guirardel's definition appropriately, one can define a "core" for a finite collection of G--actions on CAT(0) cube complexes, and recover some of the same information. The generalisation is especially faithful when G is hyperbolic, although it is also useful when G is, say, a RAAG. I'll discuss some basic properties of this object and an application to the geometry of the free splitting complex of a free group. This talk is mainly on joint work with Henry Wilton and involves some other joint work with Nicholas Touikan.