Cohomology of face rings, and torus actions
Algebraic Topology
2011-11-10 v3 Commutative Algebra
Combinatorics
Abstract
In this survey article we present several new developments of `toric topology' concerning the cohomology of face rings (also known as Stanley-Reisner algebras). We prove that the integral cohomology algebra of the moment-angle complex Z_K (equivalently, of the complement U(K) of the coordinate subspace arrangement) determined by a simplicial complex K is isomorphic to the Tor-algebra of the face ring of K. Then we analyse Massey products and formality of this algebra by using a generalisation of Hochster's theorem. We also review several related combinatorial results and problems.
Keywords
Cite
@article{arxiv.math/0506526,
title = {Cohomology of face rings, and torus actions},
author = {Taras Panov},
journal= {arXiv preprint arXiv:math/0506526},
year = {2011}
}
Comments
28 pages, more minor changes, to be published in the LMS Lecture Notes