Geodesic
Generalized Virtual Polytopes and Quasitoric Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Tome 318 (2022), pp. 139-165

Voir la notice de l'article provenant de la source Math-Net.Ru

We develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the Bernstein–Kushnirenko theorem as well as Stanley–Reisner and Pukhlikov–Khovanskii type descriptions for the cohomology rings of generalized quasitoric manifolds.
Keywords: quasitoric manifold, star-shaped sphere, virtual polytope, multi-polytope, Stanley–Reisner ring.
Mots-clés : multi-fan, moment–angle complex 
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     author = {Ivan Yu. Limonchenko and Leonid V. Monin and Askold G. Khovanskii},
     title = {Generalized {Virtual} {Polytopes} and {Quasitoric} {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {139--165},
     publisher = {mathdoc},
     volume = {318},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_318_a8/}
}
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Ivan Yu. Limonchenko; Leonid V. Monin; Askold G. Khovanskii. Generalized Virtual Polytopes and Quasitoric Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Tome 318 (2022), pp. 139-165. http://geodesic.mathdoc.fr/item/TM_2022_318_a8/