FAQ on the g-theorem and the hard Lefschetz theorem for face rings
Combinatorics
2019-08-23 v6 Commutative Algebra
Algebraic Geometry
Geometric Topology
Abstract
This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the -theorem. We review the hard Lefschetz theorem for simplicial spheres, as well as the theory at its core: perturbations of maps, biased Poincar\'e pairings and a cobordism argument that relates the Lefschetz property of a manifold to the Lefschetz property on its boundary. We also sketch an alternative argument based on edge-contractions.
Keywords
Cite
@article{arxiv.1906.05859,
title = {FAQ on the g-theorem and the hard Lefschetz theorem for face rings},
author = {Karim Adiprasito},
journal= {arXiv preprint arXiv:1906.05859},
year = {2019}
}
Comments
Overview article, 15 pages. Adds alternative proof via edge contractions