Geodesic
Stanley–Reisner rings of generalized truncation polytopes and their moment–angle manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 207-218 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider simple polytopes $P=\mathrm{vc}^k(\Delta^{n_1}\times\dots\times\Delta^{n_r})$ for $n_1\ge\dots\ge n_r\ge1$, $r\ge1$, and $k\ge0$, that is, $k$-vertex cuts of a product of simplices, and call them generalized truncation polytopes. For these polytopes we describe the cohomology ring of the corresponding moment–angle manifold $\mathcal Z_P$ and explore some topological consequences of this calculation. We also examine minimal non-Golodness for their Stanley–Reisner rings and relate it to the property of $\mathcal Z_P$ being a connected sum of sphere products. 
@article{TM_2014_286_a8,
     author = {I. Yu. Limonchenko},
     title = {Stanley{\textendash}Reisner rings of generalized truncation polytopes and their moment{\textendash}angle manifolds},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {207--218},
     year = {2014},
     volume = {286},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_286_a8/}
}
TY  - JOUR
AU  - I. Yu. Limonchenko
TI  - Stanley–Reisner rings of generalized truncation polytopes and their moment–angle manifolds
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2014
SP  - 207
EP  - 218
VL  - 286
UR  - http://geodesic.mathdoc.fr/item/TM_2014_286_a8/
LA  - ru
ID  - TM_2014_286_a8
ER  - 
%0 Journal Article
%A I. Yu. Limonchenko
%T Stanley–Reisner rings of generalized truncation polytopes and their moment–angle manifolds
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2014
%P 207-218
%V 286
%U http://geodesic.mathdoc.fr/item/TM_2014_286_a8/
%G ru
%F TM_2014_286_a8
I. Yu. Limonchenko. Stanley–Reisner rings of generalized truncation polytopes and their moment–angle manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 207-218. http://geodesic.mathdoc.fr/item/TM_2014_286_a8/

[1] Berglund A., Jöllenbeck M., “On the Golod property of Stanley–Reisner rings”, J. Algebra, 315:1 (2007), 249–273 | DOI | MR | Zbl

[2] Bosio F., Meersseman L., “Real quadrics in $\mathbf C^n$, complex manifolds and convex polytopes”, Acta math., 197:1 (2006), 53–127 | DOI | MR | Zbl

[3] Bukhshtaber V.M., Panov T.E., Toricheskie deistviya v topologii i kombinatorike, MTsNMO, M., 2004 | MR

[4] Buchstaber V.M., Panov T.E., Toric topology, E-print, 2012, arXiv: 1210.2368 [math.AT] | MR

[5] Choi S., “Different moment–angle manifolds arising from two polytopes having the same bigraded Betti numbers”, Algebr. Geom. Topol., 13:6 (2013), 3639–3649, arXiv: 1209.0515 [math.AT] | DOI | MR | Zbl

[6] Gitler S., López de Medrano S., “Intersections of quadrics, moment–angle manifolds and connected sums”, Geom. Topol., 17:3 (2013), 1497–1534, arXiv: 0901.2580 [math.GT] | DOI | MR | Zbl

[7] Golod E.S., “O gomologiyakh nekotorykh lokalnykh kolets”, DAN SSSR, 144:3 (1962), 479–482 | MR | Zbl

[8] Grayson D., Stillman M., Macaulay2: A software system for research in algebraic geometry, http://www.math.uiuc.edu/Macaulay2/

[9] Grbić J., Panov T., Theriault S., Wu J., Homotopy types of moment–angle complexes for flag complexes, E-print, 2012, arXiv: 1211.0873 [math.AT]

[10] Limonchenko I.Yu., “Bigraduirovannye chisla Betti nekotorykh prostykh mnogogrannikov”, Mat. zametki, 94:3 (2013), 373–388 | DOI | MR | Zbl

[11] McGavran D., “Adjacent connected sums and torus actions”, Trans. Amer. Math. Soc., 251 (1979), 235–254 | DOI | MR | Zbl

[12] Panov T.E., “Cohomology of face rings, and torus actions”, Surveys in contemporary mathematics, LMS Lect. Note Ser., 347, Cambridge Univ. Press, Cambridge, 2008, 165–201, arXiv: math/0506526 [math.AT] | MR | Zbl

[13] Stanley R.P., Combinatorics and commutative algebra, Prog. Math., 41, 2nd ed., Birkhäuser, Boston, 1996 | MR | Zbl

[14] Terai N., Hibi T., “Computation of Betti numbers of monomial ideals associated with stacked polytopes”, Manuscr. math., 92:4 (1997), 447–453 | DOI | MR | Zbl