Maeda, Hiroshi; Masuda, Mikiya; Panov, Taras Torus graphs and simplicial posets. (English) Zbl 1119.55004 Adv. Math. 212, No. 2, 458-483 (2007). The authors define the notion of torus graph as a regular \(n\)-valent graph with vector labels on its edges, associated to a manifold acted on by the torus. It allows them to translate the important topological properties of torus manifolds into the language of combinatorics. The notion of equivariant cohomology of a torus graph is introduced and it is shown 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 an application, it is proved that a simplicial poset is Cohen-Macaulay if its face ring is Cohen-Macaulay and thus the algebraic characterisation of Cohen-Macaulay posets is complete. Blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view are also studied. Reviewer: Gheorghe Pitiş (Braşov) Cited in 17 Documents MSC: 55N91 Equivariant homology and cohomology in algebraic topology 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 06A11 Algebraic aspects of posets Keywords:torus graph; torus manifold; simplicial poset; equivariant cohomology; Thom class; blow-up × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Bruns, Winfried; Herzog, Jürgen, Cohen-Macaulay Rings, Cambridge Stud. Adv. Math., vol. 39 (1998), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0909.13005 [2] Buchstaber, Victor M.; Panov, Taras E., Torus Actions and Their Applications in Topology and Combinatorics, Univ. Lecture Ser., vol. 24 (2002), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI · Zbl 1012.52021 [3] Buchstaber, Victor M.; Panov, Taras E., Combinatorics of simplicial cell complexes and torus actions, Tr. Mat. Inst. Steklova. Tr. Mat. Inst. Steklova, Proc. Steklov Inst. 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