|
|
|
Список литературы
|
|
|
1. |
J. F. Adams, P. J. Hilton, “On the chain algebra of a loop space”, Comment. Math. Helv., 30 (1956), 305–330 |
2. |
C. Allday, “Rational Whitehead products and a spectral sequence of Quillen. II”, Houston J. Math., 3 (1977), 301–308 |
3. |
D. J. Anick, “Hopf algebras up to homotopy”, J. Amer. Math. Soc., 2:3 (1989), 417–453 |
4. |
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., 225:3 (2010), 1634–1668 |
5. |
A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler, “Cup-products for the polyhedral product functor”, Math. Proc. Cambridge Philos. Soc., 153:3 (2012), 457–469 |
6. |
A. Bahri, M. Bendersky, F. R. Cohen, S. Gitler, On the rational homotopy type of moment-angle complexes, 2012, 6 pp., arXiv: 1206.2173 |
7. |
И. В. Баскаков, В. М. Бухштабер, Т. Е. Панов, “Алгебры клеточных коцепей и действия торов”, УМН, 59:3(357) (2004), 159–160 ; англ. пер.: I. V. Baskakov, V. M. Bukhshtaber, T. E. Panov, “Cellular cochain algebras and torus actions”, Russian Math. Surveys, 59 (2004), 562–563 |
8. |
P. Beben, J. Grbić, Configuration spaces and polyhedral products, 2016 (v1 – 2014), 32 pp., arXiv: 1409.4462 |
9. |
A. Berglund, M. Jöllenbeck, “On the Golod property of Stanley–Reisner rings”, J. Algebra, 315:1 (2007), 249–273 |
10. |
A. Björner, M. L. Wachs, “Shellable nonpure complexes and posets. I”, Trans. Amer. Math. Soc., 348:4 (1996), 1299–1327 |
11. |
A. Björner, M. Wachs, V. Welker, “On sequentially Cohen–Macaulay complexes and posets”, Israel J. Math., 169 (2009), 295–316 |
12. |
F. Bosio, L. Meersseman, “Real quadrics in $\mathbf{C}^{n}$, complex manifolds and convex polytopes”, Acta Math., 197:1 (2006), 53–127 |
13. |
P. Bubenik, “Separated Lie models and the homotopy Lie algebra”, J. Pure Appl. Algebra, 212:2 (2008), 401–410 |
14. |
В. М. Бухштабер, Т. Е. Панов, “Действия торов, комбинаторная топология и гомологическая алгебра”, УМН, 55:5(335) (2000), 3–106 ; англ. пер.: V. M. Bukhshtaber, T. E. Panov, “Torus actions, combinatorial topology, and homological algebra”, Russian Math. Surveys, 55 (2000), 825–921 |
15. |
V. M. Buchstaber, T. E. Panov, “Torus actions and their applications in topology and combinatorics”, Univ. Lecture Ser., 24, Amer. Math. Soc., Providence, RI, 2002, viii+144 pp. |
16. |
F. R. Cohen, J. C. Moore, J. A. Neisendorfer, “Torsion in homotopy groups”, Ann. of Math. (2), 109:1 (1979), 121–168 |
17. |
S. Choi, M. Masuda, D. Y. Suh, “Rigidity problems in toric topology: a survey”, Классическая и современная математика в поле деятельности Бориса Николаевича Делоне, Сборник статей. К 120-летию со дня рождения члена-корреспондента АН СССР Бориса Николаевича Делоне, Тр. МИАН, 275, МАИК, М., 2011, 188–201 ; Proc. Steklov Inst. Math., 275 (2011), 177–190 |
18. |
M. W. Davis, T. Januszkiewicz, “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 |
19. |
G. Denham, A. I. Suciu, “Moment-angle complexes, monomial ideals and Massey products”, Pure Appl. Math. Q., 3:1 (2007), 25–60 |
20. |
N. Dobrinskaya, Loops on polyhedral products and diagonal arrangements, 2009, 32 pp., arXiv: 0901.2871 |
21. |
Y. Félix, D. Tanré, “Rational homotopy of the polyhedral product functor”, Proc. Amer. Math. Soc., 137:3 (2009), 891–898 |
22. |
M. Franz, “The integral cohomology of toric manifolds”, Геометрическая топология, дискретная геометрия и теория множеств, Сборник статей, Тр. МИАН, 252, Наука, М., 2006, 61–70 ; Proc. Steklov Inst. Math., 252 (2006), 53–62 |
23. |
T. Ganea, “A generalisation of the homology and homotopy suspension”, Comment. Math. Helv., 39 (1965), 295–322 |
24. |
S. Gitler, S. López de Medrano, “Intersections of quadrics, moment-angle manifolds and connected sums”, Geom. Topol., 17:3 (2013), 1497–1534 ; (2012 (v1 – 2009)), 45 pp., arXiv: 0901.2580 |
25. |
Е. С. Голод, “О гомологиях некоторых локальных колец”, Докл. АН СССР, 144:3 (1962), 479–482 ; англ. пер.: E. S. Golod, “On the homology of some local rings”, Soviet Math. Dokl., 3 (1962), 745–749 |
26. |
J. Grbić, T. Panov, S. Theriault, Jie Wu, “The homotopy types of moment-angle complexes for flag complexes”, Trans. Amer. Math. Soc., 368:9 (2016), 6663–6682 ; (2014 (v1 – 2012)), 20 pp., arXiv: 1211.0873 |
27. |
Е. Грбич, С. Терио, “Гомотопический тип дополнения конфигурации координатных подпространств коразмерности два”, УМН, 59:6(360) (2004), 203–204 ; англ. пер.: J. Grbić, S. Theriault, “Homotopy type of the complement of a coordinate subspace arrangement of codimension two”, Russian Math. Surveys, 59:6 (2004), 1207–1209 |
28. |
J. Grbić, S. Theriault, “The homotopy type of the complement of a coordinate subspace arrangement”, Topology, 46:4 (2007), 357–396 |
29. |
J. Grbić, S. Theriault, “The homotopy type of the polyhedral product for shifted complexes”, Adv. Math., 245 (2013), 690–715 |
30. |
V. Grujić, V. Welker, Discrete Morse theory for moment-angle complexes of pairs $(D^{n},S^{n-1})$, 2012, 19 pp., arXiv: 1212.2028 |
31. |
J. Herzog, V. Reiner, V. Welker, “Componentwise linear ideals and Golod rings”, Michigan Math. J., 46:2 (1999), 211–223 |
32. |
K. Iriye, D. Kishimoto, “Decompositions of polyhedral products for shifted complexes”, Adv. Math., 245 (2013), 716–736 |
33. |
K. Iriye, D. Kishimoto, Topology of polyhedral products and the Golod property of Stanley–Reisner rings, 2013, 17 pp., arXiv: 1306.6221 |
34. |
I. M. James, “Reduced product spaces”, Ann. of Math. (2), 62 (1955), 170–197 |
35. |
J.-M. Lemaire, Algèbres connexes et homologie des espaces de lacets, Lecture Notes in Math., 422, Springer-Verlag, Berlin–New York, 1974, xiv+134 pp. |
36. |
И. Ю. Лимонченко, “Кольца Стенли–Райснера обобщенных многогранников усечения и их момент–угол-многообразия”, Алгебраическая топология, выпуклые многогранники и смежные вопросы, К 70-летию со дня рождения члена-корреспондента РАН Виктора Матвеевича Бухштабера, Тр. МИАН, 286, МАИК, М., 2014, 207–218 ; англ. пер.: I. Yu. Limonchenko, “Stanley–Reisner rings of generalized truncation polytopes and their moment-angle manifolds”, Proc. Steklov Inst. Math., 286 (2014), 188–197 |
37. |
И. Ю. Лимонченко, “Семейства минимально неголодовских комплексов и полиэдральные произведения”, Дальневост. матем. журн., 15:2 (2015), 222–237 |
38. |
Z. Lü, T. Panov, “Moment-angle complexes from simplicial posets”, Cent. Eur. J. Math., 9:4 (2011), 715–730 |
39. |
D. McGavran, “Adjacent connected sums and torus actions”, Trans. Amer. Math. Soc., 251 (1979), 235–254 |
40. |
H. Maeda, M. Masuda, T. Panov, “Torus graphs and simplicial posets”, Adv. Math., 212:2 (2007), 458–483 |
41. |
J. W. Milnor, J. C. Moore, “On the structure of Hopf algebras”, Ann. of Math. (2), 81:2 (1965), 211–264 |
42. |
D. Notbohm, N. Ray, “On Davis–Januszkiewicz homotopy types. I. Formality and rationalisation”, Algebr. Geom. Topol., 5 (2005), 31–51 |
43. |
T. E. Panov, N. Ray, “Categorical aspects of toric topology”, Toric topology, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008, 293–322 |
44. |
G. J. Porter, “Higher order Whitehead products”, Topology, 3:2 (1965), 123–135 |
45. |
G. J. Porter, “The homotopy groups of wedges of suspensions”, Amer. J. Math., 88:3 (1966), 655–663 |
46. |
D. Quillen, “Rational homotopy theory”, Ann. of Math. (2), 90:2 (1969), 205–295 |
47. |
R. P. Stanley, “$f$-vectors and $h$-vectors of simplicial posets”, J. Pure Appl. Algebra, 71:2-3 (1991), 319–331 |
48. |
S. Theriault, “Moment-angle manifolds and Panov's problem”, Int. Math. Res. Not. IMRN, 2015:20 (2015), 10154–10175 |
49. |
A. J. Trevisan, “Generalized Davis–Januszkiewicz spaces, multicomplexes and monomial rings”, Homology Homotopy Appl., 13:1 (2011), 205–221 |