The Hard Lefschetz Theorem for PL spheres
Combinatorics
2019-08-06 v6 Commutative Algebra
Algebraic Geometry
Geometric Topology
Abstract
We provide a simpler proof of the hard Lefschetz Theorem for face rings of PL spheres: While the algebraic theory remains the same, we replace the geometric constructions by Pachner's Theorem. This simplifies the reasoning for an important special case of the main result of the first author in arxiv:1812.10454, and already implies the McMullen g-conjecture for PL spheres, as well as the Gr\"unbaum-Kalai-Sarkaria conjecture.
Cite
@article{arxiv.1906.00737,
title = {The Hard Lefschetz Theorem for PL spheres},
author = {Karim Adiprasito and Johanna K. Steinmeyer},
journal= {arXiv preprint arXiv:1906.00737},
year = {2019}
}
Comments
subsumed into arXiv:1906.05859