Homology groups and homotopy types of lattices

This talk will be about extensions of Rota's formula for the Möbius function of a geometric lattice in terms of sets containing no broken circuit (NBC sets). The extensions in question include one by Björner describing the homology of a geometric lattice in terms of NBC sets, another by Sagan and me extending Rota's formula to non-geometric lattices, and another by Segev describing the homotopy type of the order complex of a finite lattice. I'll present a more general and more explicit version of Segev's result, which implies a Björner-like description of the homology of arbitrary finite lattices.