Weak Lefschetz property of PL-spheres

Abstract

A recent result of Papadakis-Petrotou shows that every simplicial sphere has the weak Lefschetz property in characteristic $2$. In this paper, we give a simpler proof of this result for PL-spheres by showing that the weak Lefschetz property in characteristic $2$ is preserved by bistellar moves. Several applications are given.

14 pages; In version 7, there is a wrong computation at the end of the proof of Theorem 3.2, but this mistake can be fixed by assuming the field has characteristic 2. So the abstract and the statement of the main theorem are changed in this version

References in corpus (3)

• Combinatorial Lefschetz theorems beyond positivity
• The characteristic 2 anisotropicity of simplicial spheres
• On the Complexity of Embeddable Simplicial Complexes