Lukas Brantner: Buildings in Characteristic 1 and p via Discrete Morse Theory

We introduce a technique we call "complementary contraction“ and demonstrate its applicability by computing various equivariant posets of interest in a uniform manner: the fixed point spaces of the partition complex, the parabolic restriction of BT buildings in characteristic p, and the Young restrictions of the partition complex (thereby giving a short and purely combinatorial proof of a recent theorem of Arone).

If time permits, we describe a normaliser decomposition for G-spaces (generalising a construction of Dwyer for spaces BG) and illustrate how it can be used to deduce information about strict orbits from information about homotopy orbits in a concrete example.