Stanley--Reisner rings of generalized truncation polytopes and their moment--angle manifolds
Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 207-218.

Voir la notice de l'article provenant de la source Math-Net.Ru

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{TRSPY_2014_286_a8,
     author = {I. Yu. Limonchenko},
     title = {Stanley--Reisner rings of generalized truncation polytopes and their moment--angle manifolds},
     journal = {Informatics and Automation},
     pages = {207--218},
     publisher = {mathdoc},
     volume = {286},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a8/}
}
TY  - JOUR
AU  - I. Yu. Limonchenko
TI  - Stanley--Reisner rings of generalized truncation polytopes and their moment--angle manifolds
JO  - Informatics and Automation
PY  - 2014
SP  - 207
EP  - 218
VL  - 286
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a8/
LA  - ru
ID  - TRSPY_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 Informatics and Automation
%D 2014
%P 207-218
%V 286
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a8/
%G ru
%F TRSPY_2014_286_a8
I. Yu. Limonchenko. Stanley--Reisner rings of generalized truncation polytopes and their moment--angle manifolds. Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 207-218. http://geodesic.mathdoc.fr/item/TRSPY_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