Garland's Technique for Posets and High Dimensional Grassmannian Expanders

Understand

Local to global machinery plays an important role in the study of simplicial complexes, since the seminal work of Garland [G] to our days.

• In this work we develop a local to global machinery for general posets.
• We show that the high dimensional expansion notions and many recent expansion results have a generalization to posets.
• Examples are fast convergence of high dimensional random walks generalizing [KO,AL], an equivalence with a global random walk definition, generalizing [DDFH] and a trickling down theorem, generalizing [O].