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A generalization of moment-angle manifolds with noncontractible orbit spaces

Li Yu

Algebraic & Geometric Topology 24 (2024) 449–492
Bibliography
1 A A Ayzenberg, V M Buchstaber, Nerve complexes and moment-angle spaces of convex polytopes, Tr. Mat. Inst. Steklova 275 (2011) 22 MR2962969
2 A Ayzenberg, M Masuda, S Park, H Zeng, Cohomology of toric origami manifolds with acyclic proper faces, J. Symplectic Geom. 15 (2017) 645 MR3696587
3 A Bahri, M Bendersky, F R Cohen, S Gitler, The polyhedral product functor: a method of decomposition for moment-angle complexes, arrangements and related spaces, Adv. Math. 225 (2010) 1634 MR2673742
4 A Bahri, M Bendersky, F R Cohen, S Gitler, Cup-products for the polyhedral product functor, Math. Proc. Cambridge Philos. Soc. 153 (2012) 457 MR2990625
5 A Bahri, M Bendersky, F R Cohen, S Gitler, A spectral sequence for polyhedral products, Adv. Math. 308 (2017) 767 MR3600073
6 A Bahri, M Bendersky, F R Cohen, S Gitler, A Cartan formula for the cohomology of polyhedral products and its application to the ring structure, preprint (2020) arXiv:2009.06818
7 I V Baskakov, V M Buchstaber, T E Panov, Algebras of cellular cochains, and torus actions, Uspekhi Mat. Nauk 59 (2004) 159 MR2117435
8 V M Buchstaber, T E Panov, Actions of tori, combinatorial topology and homological algebra, Uspekhi Mat. Nauk 55 (2000) 3 MR1799011
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, Toric topology, 204, Amer. Math. Soc. (2015) MR3363157
11 L Cai, On products in a real moment-angle manifold, J. Math. Soc. Japan 69 (2017) 503 MR3638276
12 A Cannas da Silva, V Guillemin, A R Pires, Symplectic origami, Int. Math. Res. Not. 2011 (2011) 4252 MR2836021
13 W L Chow, On unmixedness theorem, Amer. J. Math. 86 (1964) 799 MR0171804
14 M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293 MR0690848
15 M W Davis, The homology of a space on which a reflection group acts, Duke Math. J. 55 (1987) 97 MR0883665
16 M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474
17 M W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417 MR1104531
18 M Franz, The integral cohomology of toric manifolds, Proc. Steklov Inst. Math. 252 (2006) 53 MR2255969
19 R Fröberg, L T Hoa, Segre products and Rees algebras of face rings, Comm. Algebra 20 (1992) 3369 MR1186713
20 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
21 L T Hoa, On Segre products of affine semigroup rings, Nagoya Math. J. 110 (1988) 113 MR0945909
22 T S Holm, A R Pires, The topology of toric origami manifolds, Math. Res. Lett. 20 (2013) 885 MR3207359
23 I M James, Reduced product spaces, Ann. of Math. 62 (1955) 170 MR0073181
24 T Januszkiewicz, Actions with section, lecture (2020)
25 F E A Johnson, On the triangulation of stratified sets and singular varieties, Trans. Amer. Math. Soc. 275 (1983) 333 MR0678354
26 Z Lü, T Panov, Moment-angle complexes from simplicial posets, Cent. Eur. J. Math. 9 (2011) 715 MR2805305
27 M Masuda, T Panov, On the cohomology of torus manifolds, Osaka J. Math. 43 (2006) 711 MR2283418
28 E Miller, B Sturmfels, Combinatorial commutative algebra, 227, Springer (2005) MR2110098
29 M Poddar, S Sarkar, A class of torus manifolds with nonconvex orbit space, Proc. Amer. Math. Soc. 143 (2015) 1797 MRMR3314091
30 R P Stanley, Combinatorics and commutative algebra, 41, Birkhäuser (1996) MR1453579
31 R M Vogt, Homotopy limits and colimits, Math. Z. 134 (1973) 11 MR0331376
32 X Wang, Q Zheng, The homology of simplicial complements and the cohomology of polyhedral products, Forum Math. 27 (2015) 2267 MR3365798
33 V Welker, G M Ziegler, R T Živaljević, Homotopy colimits: comparison lemmas for combinatorial applications, J. Reine Angew. Math. 509 (1999) 117 MR1679169
34 G W Whitehead, Homotopy groups of joins and unions, Trans. Amer. Math. Soc. 83 (1956) 55 MR0080918
35 T Yoshida, Local torus actions modeled on the standard representation, Adv. Math. 227 (2011) 1914 MR2803791
36 L Yu, On Hochster’s formula for a class of quotient spaces of moment-angle complexes, Osaka J. Math. 56 (2019) 33 MR3908775
37 Q Zheng, The cohomology algebra of polyhedral product spaces, J. Pure Appl. Algebra 220 (2016) 3752 MR3506479
38 G M Ziegler, R T Živaljević, Homotopy types of subspace arrangements via diagrams of spaces, Math. Ann. 295 (1993) 527 MR1204836