Generalized non-crossing partitions and buildings

For every finite reflection group W, the noncrossing partitions NC(W) are a lattice in the absolutely ordered group W. In the case of the symmetric group, T. Brady and J. McCammond showed that the order complex of NC(W) embeds into a spherical building. In joint work with P. Schwer, we generalized the theorem for all finite reflection groups. Interpreting NC(W) as a subcomplex of a spherical building now enables us to better understand the building-like structure of NC(W).