FAQ on the g-theorem and the hard Lefschetz theorem for face rings
Karim Adiprasito

Abstract. We discuss the hard Lefschetz theorem for simplicial spheres, as well as the theory at its core: perturbations of maps, biased Poincaré pairings and a cobordism argument that relates the Lefschetz property of a manifold to the Lefschetz property on its boundary, and sketch an alternative argument based on edge contractions.

Rend. Mat. Appl. (7) 40 (2019) 97-111; pdf