Torus graphs and simplicial posets

Hiroshi Maeda; Mikiya Masuda; Taras Panov

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Torus graphs and simplicial posets

Hiroshi Maeda·Mikiya Masuda·Taras Panov

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Abstract

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.

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BibTeX RIS

Hiroshi Maeda, Mikiya Masuda, Taras Panov. 2005-11-23. Torus graphs and simplicial posets. https://arxiv.org/abs/math/0511582

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