Cohomology of face rings, and torus actions

Details Cohomology of face rings, and torus actions Cohomology of face rings, and torus actions

2005-06-25

arxiv.org/abs/math/0506526v3

London Math. Soc. Lecture Note Series 347 (2008), 165-201

Mathematics

Algebraic Topology

28 pages, more minor changes, to be published in the LMS Lecture Notes

Scientific paper

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.

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