Geodesic
Stellar Subdivision and Polyhedral Products
Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 314-329

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

We consider the homotopy theory of polyhedral products arising from the operation of stellar subdivision on simplicial complexes. In the special case of polyhedral products formed from pairs $(S^{n_i},*)$ where the $S^{n_i}$'s are simply connected spheres, information is deduced about the growth of the rational and torsion homotopy groups.
Mots-clés : homotopy type
Keywords: polyhedral product, simplicial complex, stellar subdivision. 
Stephen Theriault. Stellar Subdivision and Polyhedral Products. Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 314-329. http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a13/
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[1] Bahri A., Bendersky M., Cohen F.R., Gitler S., “The polyhedral product functor: A method of decomposition for moment–angle complexes, arrangements and related spaces”, Adv. Math., 225:3 (2010), 1634–1668 | DOI | MR | Zbl

[2] Bahri A., Bendersky M., Cohen F.R., Gitler S., “Cup-products for the polyhedral product functor”, Math. Proc. Cambridge Philos. Soc., 153:3 (2012), 457–469 | DOI | MR | Zbl

[3] Boyde G., “$p$-Hyperbolicity of homotopy groups via $K$-theory”, Math. Z., 301:1 (2022), 977–1009 | DOI | MR | Zbl

[4] Boyde G., “$\mathbb {Z}/p^r$-hyperbolicity via homology”, Isr. J. Math., 260:1 (2024), 141–193 ; arXiv: 2106.03516 [math.AT] | DOI | MR | Zbl | DOI

[5] Cohen F.R., Moore J.C., Neisendorfer J.A., “Torsion in homotopy groups”, Ann. Math. Ser. 2, 109:1 (1979), 121–168 | DOI | MR | Zbl

[6] Cohen F.R., Moore J.C., Neisendorfer J.A., “The double suspension and exponents of the homotopy groups of spheres”, Ann. Math. Ser. 2, 110:3 (1979), 549–565 | DOI | MR | Zbl

[7] Denham G., Suciu A.I., “Moment–angle complexes, monomial ideals and Massey products”, Pure Appl. Math. Q., 3:1 (2007), 25–60 | DOI | MR | Zbl

[8] Félix Y., Halperin S., Thomas J.-C., “The homotopy Lie algebra for finite complexes”, Publ. math. Inst. hautes étud. sci., 56 (1982), 179–202 | DOI | MR | Zbl

[9] Félix Y., Tanré D., “Rational homotopy of the polyhedral product functor”, Proc. Am. Math. Soc., 137:3 (2009), 891–898 | DOI | MR | Zbl

[10] Ganea T., “A generalization of the homology and homotopy suspension”, Comment. math. Helv., 39 (1965), 295–322 | DOI | MR | Zbl

[11] Grbić J., Theriault S., “The homotopy type of the complement of a coordinate subspace arrangement”, Topology, 46:4 (2007), 357–396 | DOI | MR | Zbl

[12] Grbić J., Theriault S., “The homotopy type of the polyhedral product for shifted complexes”, Adv. Math., 245 (2013), 690–715 | DOI | MR | Zbl

[13] Hao Y., Sun Q., Theriault S., “Moore's conjecture for polyhedral products”, Math. Proc. Cambridge Philos. Soc., 167:1 (2019), 23–33 | DOI | MR | Zbl

[14] Huang R., Wu J., “Exponential growth of homotopy groups of suspended finite complexes”, Math. Z., 295:3–4 (2020), 1301–1321 | DOI | MR | Zbl

[15] Iriye K., Kishimoto D., “Fat-wedge filtration and decomposition of polyhedral products”, Kyoto J. Math., 59:1 (2019), 1–51 | DOI | MR | Zbl

[16] Mather M., “Pull-backs in homotopy theory”, Can. J. Math., 28:2 (1976), 225–263 | DOI | MR | Zbl

[17] Neisendorfer J.A., Selick P.S., “Some examples of spaces with or without exponents”, Current trends in algebraic topology: Semin. London/Ont., 1981, CMS Conf. Proc., 2, Part 1, Am. Math. Soc., Providence, RI, 1982, 343–357 | MR

[18] T. E. Panov and Ya. A. Veryovkin, “Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups”, Sb. Math., 207:11 (2016), 1582–1600 | DOI | DOI | MR | Zbl

[19] Porter G.J., “The homotopy groups of wedges of suspensions”, Am. J. Math., 88:3 (1966), 655–663 | DOI | MR | Zbl

[20] Selick P., “2-primary exponents for the homotopy groups of spheres”, Topology, 23:1 (1984), 97–99 | DOI | MR | Zbl

[21] S. Theriault, “Polyhedral products for connected sums of simplicial complexes”, Proc. Steklov Inst. Math., 317 (2022), 151–160 | DOI | DOI | MR | Zbl

[22] Theriault S., “Polyhedral products for wheel graphs and their generalizations”, Toric topology and polyhedral products, Fields Inst. Commun., 89, Springer, Cham, 2024, 295–311 | DOI | MR | Zbl