BIRS Workshop Lecture Videos
Discrete Morse Theory and André–Quillen Homology Brantner, Lukas
We use discrete Morse theory to prove a complementation formula (originally discovered by Björner-Walker) and demonstrate its applicability by computing various equivariant posets of interest in a uniform manner: fixed point spaces of the partition complex, parabolic restrictions of BT buildings in characteristic \(p\), and Young restrictions of the partition complex (thereby giving a short and purely combinatorial proof of a recent theorem of Arone). In joint work with Arone, we link these computations to `AQ for commutative monoid spaces' and provide space-level models for results of Goerss for AQ.
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