Surveys in Contemporary Mathematics: Cohomology of face rings, and torus actions
By T. Panov. 2005
66 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ace200a5ea44bc47e63c1afb3a5e93f80b9a8265
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
- S. Gitler
- A. Bahri
- Frédéric Bosio
- Martin Bendersky
- Frederick R. Cohen
- L. Meersseman
- T. Panov
- Santiago López de Medrano
In Geometry and Topology
- S. Gitler
- Frédéric Bosio
- A. Bahri
- Martin Bendersky
- Frederick R. Cohen
- L. Meersseman
- T. Panov
- V. Buchstaber
Citations in the corpus
- The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces (2007, methodology): “MacPherson [20], Hochster [22], Baskakov [3], Panov [ 36 ], Buchstaber-Panov [7] and Franz [17, 18].”
- Real quadrics in Cn, complex manifolds and convex polytopes (2006, methodology): “that the LV-M manifolds are not formal (see also [ 35 ]), so that in fact the techniques of [13] cannot be applied.”