Torus graphs and simplicial posets

• Autores: Hiroshi Maeda, Mikiya Masuda, Taras Panov
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 2, 2007, págs. 458-483
• Idioma: inglés
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• Resumen

  • For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated simplicial poset. This extends a series of previous results on the equivariant cohomology of torus manifolds. As a primary combinatorial application, we show that a simplicial poset is Cohen¿Macaulay if its face ring is Cohen¿Macaulay. This completes the algebraic characterisation of Cohen¿Macaulay posets initiated by Stanley. We also study blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view.