Geometry & Topology Volume 25, issue 4 (2021)

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The cohomology rings of smooth toric varieties and quotients of moment-angle complexes

Matthias Franz

Geometry & Topology 25 (2021) 2109–2144

DOI: 10.2140/gt.2021.25.2109

Bibliography

1	I V Baskakov, V M Buchstaber, T E Panov, Cellular cochain algebras and torus actions, Uspekhi Mat. Nauk 59 (2004) 159 MR2117435
2	P Baum, L Smith, The real cohomology of differentiable fibre bundles, Comment. Math. Helv. 42 (1967) 171 MR221522
3	C Berger, B Fresse, Combinatorial operad actions on cochains, Math. Proc. Cambridge Philos. Soc. 137 (2004) 135 MR2075046
4	A Berglund, Homotopy invariants of Davis–Januszkiewicz spaces and moment-angle complexes, unpublished notes (2010)
5	E Bifet, C De Concini, C Procesi, Cohomology of regular embeddings, Adv. Math. 82 (1990) 1 MR1057441
6	G E Bredon, Introduction to compact transformation groups, 46, Academic (1972) MR0413144
7	V M Buchstaber, T E Panov, Algebraic topology of manifolds defined by simple polytopes, Uspekhi Mat. Nauk 53 (1998) 195 MR1657604
8	V M Buchstaber, T E Panov, Torus actions and the combinatorics of polytopes, Tr. Mat. Inst. Steklova 225 (1999) 96 MR1725935
9	V M Buchstaber, T E Panov, Torus actions and their applications in topology and combinatorics, 24, Amer. Math. Soc. (2002) MR1897064
10	V M Buchstaber, T E Panov, Torus actions in topology and combinatorics, Mosk. Tsentr Nepreryvnogo Matematicheskogo Obrazovaniya (2004) 272 MR2078156
11	V M Buchstaber, T E Panov, Toric topology, 204, Amer. Math. Soc. (2015) MR3363157
12	L Cai, On products in a real moment-angle manifold, J. Math. Soc. Japan 69 (2017) 503 MR3638276
13	S Choi, H Park, On the cohomology and their torsion of real toric objects, Forum Math. 29 (2017) 543 MR3641664
14	S Choi, H Park, Multiplicative structure of the cohomology ring of real toric spaces, Homology Homotopy Appl. 22 (2020) 97 MR4027292
15	M W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417 MR1104531
16	D Edidin, Equivariant geometry and the cohomology of the moduli space of curves, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International (2013) 259 MR3184166
17	M Franz, Koszul duality for tori, PhD thesis, Universität Konstanz (2001)
18	M Franz, On the integral cohomology of smooth toric varieties, preprint (2003) arXiv:math/0308253
19	M Franz, The integral cohomology of toric manifolds, Tr. Mat. Inst. Steklova 252 (2006) 61 MR2255969
20	M Franz, Describing toric varieties and their equivariant cohomology, Colloq. Math. 121 (2010) 1 MR2725697
21	M Franz, The cohomology rings of homogeneous spaces, preprint (2021) arXiv:1907.04777v3
22	M Franz, Homotopy Gerstenhaber formality of Davis–Januszkiewicz spaces, preprint (2021) arXiv:1907.04782v3
23	M Franz, The cohomology rings of real toric spaces and smooth real toric varieties, preprint (2021) arXiv:2008.08961v3
24	S Gitler, S López de Medrano, Intersections of quadrics, moment-angle manifolds and connected sums, Geom. Topol. 17 (2013) 1497 MR3073929
25	J C Hausmann, Mod two homology and cohomology, Springer (2014) MR3308717
26	J Jurkiewicz, Torus embeddings, polyhedra, k^∗–actions and homology, Dissertationes Math. (Rozprawy Mat.) 236 (1985) 64 MR820078
27	T Kadeishvili, S Saneblidze, A cubical model for a fibration, J. Pure Appl. Algebra 196 (2005) 203 MR2110523
28	M de Longueville, The ring structure on the cohomology of coordinate subspace arrangements, Math. Z. 233 (2000) 553 MR1750937
29	J P May, Simplicial objects in algebraic topology, , Univ. of Chicago Press (1992) MR1206474
30	D Notbohm, N Ray, On Davis–Januszkiewicz homotopy types, I : Formality and rationalisation, Algebr. Geom. Topol. 5 (2005) 31 MR2135544
31	T E Panov, On the cohomology of quotient spaces of moment-angle complexes, Uspekhi Mat. Nauk 70 (2015) 209 MR3400574
32	T E Panov, N Ray, Categorical aspects of toric topology, from: "Toric topology" (editors M Harada, Y Karshon, M Masuda, T Panov), Contemp. Math. 460, Amer. Math. Soc. (2008) 293 MR2428364
33	S Saneblidze, The bitwisted Cartesian model for the free loop fibration, Topology Appl. 156 (2009) 897 MR2498922
34	N P Strickland, Notes on toric spaces, unpublished notes (1999)
35	A I Suciu, The rational homology of real toric manifolds, preprint (2013) arXiv:1302.2342
36	A J Trevisan, Generalized Davis–Januszkiewicz spaces and their applications to algebra and topology, PhD thesis, Vrije Universiteit Amsterdam (2012)
37	A A Voronov, M Gerstenkhaber, Higher-order operations on the Hochschild complex, Funktsional. Anal. i Prilozhen. 29 (1995) 1 MR1328534