Geodesic
Cohomology rings of a class of torus manifolds
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 81 (2020) no. 1, pp. 87-104.

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Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of locally standard torus manifolds whose orbit space may have proper non-acyclic faces. References: 15 entries. 
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S. Sarkar; D. Stanley. Cohomology rings of a class of torus manifolds. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 81 (2020) no. 1, pp. 87-104. http://geodesic.mathdoc.fr/item/MMO_2020_81_1_a2/

[1] A. Ayzenberg, M. Masuda, S. Park, H. Zeng, “Cohomology of toric origami manifolds with acyclic proper faces”, J. Symplectic Geom., 15:3 (2017), 645–685 | DOI | MR | Zbl

[2] A. Ayzenberg, “Homology cycles in manifolds with locally standard torus actions”, Homology Homotopy Appl., 18:1 (2016), 1–23 | DOI | MR | Zbl

[3] A. Ayzenberg, “Locally standard torus actions and $h'$-numbers of simplicial posets”, J. Math. Soc. Japan, 68:4 (2016), 1725–1745 | DOI | MR | Zbl

[4] V. M. Buchstaber, T. E. Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series, 24, AMS, Providence, RI, 2002 | DOI | MR | Zbl

[5] V. M. Buchstaber, N. Ray, “Tangential structures on toric manifolds, and connected sums of polytopes”, Internat. Math. Res. Notices, 4 (2001), 193–219 | DOI | MR | Zbl

[6] M. W. Davis, “Groups generated by reflections and aspherical manifolds not covered by Euclidean space”, Ann. of Math. (2), 117:2 (1983), 293–324 | DOI | MR | Zbl

[7] M. W. Davis, T. Januszkiewicz, “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 | DOI | MR | Zbl

[8] M. D. Grossberg, Y. Karshon, “Equivariant index and the moment map for completely integrable torus actions”, Adv. Math., 133:2 (1998), 185–223 | DOI | MR | Zbl

[9] A. Hattori, M. Masuda, “Theory of multi-fans”, Osaka J. Math., 40:1 (2003), 1–68 | MR | Zbl

[10] H. Ishida, Y. Fukukawa, M. Masuda, “Topological toric manifolds”, Mosc. Math. J., 13:1 (2013), 57–98 ; 189–190 | DOI | MR | Zbl

[11] D. Joyce, “On manifolds with corners”, Advances in geometric analysis, Adv. Lect. Math., 21, Int. Press, Somerville, MA, 2012, 225–258 | MR | Zbl

[12] P. Lambrechts, D. Stanley, “Algebraic models of Poincaré embeddings”, Algebr. Geom. Topol., 5 (2005), 135–182 | DOI | MR | Zbl

[13] M. Masuda, T. Panov, “On the cohomology of torus manifolds”, Osaka J. Math., 43:3 (2006), 711–746 | MR | Zbl

[14] M. Poddar, S. Sarkar, “A class of torus manifolds with nonconvex orbit space”, Proc. Amer. Math. Soc., 143:4 (2015), 1797–1811 | DOI | MR | Zbl

[15] T. Yoshida, “Local torus actions modeled on the standard representation”, Adv. Math., 227:5 (2011), 1914–1955 | DOI | MR | Zbl