Abstract:
We construct and study polyhedral product models for classifying spaces of right-angled Artin and Coxeter groups, general graph product groups and their commutator subgroups. By way of application, we give a criterion for the commutator subgroup of a graph product group to be free, and provide an explicit minimal set of generators for the commutator subgroup of a right-angled Coxeter group.
Bibliography: 21 titles.
The research of the first author was carried out at the Institute for Information Transmission Problems of Russian Academy of Sciences and was supported by the Russian Science Foundation (grant no. 14-50-00150). The research of the second author was supported by the Russian Foundation for Basic Research (grant no. 14-01-00537-а).
Citation:
T. E. Panov, Ya. A. Veryovkin, “Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups”, Sb. Math., 207:11 (2016), 1582–1600
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\paper Polyhedral products and commutator subgroups of right-angled Artin and Coxeter groups
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\issue 11
\pages 1582--1600
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Linking options:
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This publication is cited in the following 24 articles:
Ya. A. Veryovkin, T. A. Rahmatullaev, “On consecutive factors of the lower central series of right-angled Coxeter groups”, Math. Notes, 116:1 (2024), 10–29
Pravin Kumar, Tushar Kanta Naik, Neha Nanda, Mahender Singh, “Commutator subgroups and crystallographic quotients of virtual extensions of symmetric groups”, Journal of Pure and Applied Algebra, 228:11 (2024), 107713
Stephen Theriault, “Stellar Subdivision and Polyhedral Products”, Proc. Steklov Inst. Math., 326 (2024), 289–302
Taras E. Panov, Temurbek A. Rahmatullaev, “Polyhedral Products, Graph Products, and pp-Central Series”, Proc. Steklov Inst. Math., 326 (2024), 269–285
Vardan Oganesyan, “Zoo of monotone Lagrangians in CPn”, Sel. Math. New Ser., 29:5 (2023)
N. Yu. Erokhovets, “Canonical geometrization of orientable 3-manifolds defined by vector colourings of 3-polytopes”, Sb. Math., 213:6 (2022), 752–793
Grbic J., Simmons G., Ilyasova M., Panov T., “One-Relator Groups and Algebras Related to Polyhedral Products”, Proc. R. Soc. Edinb. Sect. A-Math., 152:1 (2022), 128–147
Taras E. Panov, Indira K. Zeinikesheva, “Equivariant Cohomology of Moment–Angle Complexes with Respect to Coordinate Subtori”, Proc. Steklov Inst. Math., 317 (2022), 141–150
Stephen Theriault, “Polyhedral Products for Connected Sums of Simplicial Complexes”, Proc. Steklov Inst. Math., 317 (2022), 151–160
F. E. Vylegzhanin, “Pontryagin Algebras and the LS-Category of Moment–Angle Complexes in the Flag Case”, Proc. Steklov Inst. Math., 317 (2022), 55–77
Ya. A. Veryovkin, “Graded Components of the Lie Algebra Associated with the Lower Central Series of a Right-Angled Coxeter Group”, Proc. Steklov Inst. Math., 318 (2022), 26–37
L. Wu, L. Yu, “Fundamental groups of small covers revisited”, Int. Math. Res. Notices, 2021:10 (2021), 7262–7298
N. Yu. Erokhovets, “Theory of families of polytopes: fullerenes and Pogorelov polytopes”, Moscow University Mathematics Bulletin, 76:2 (2021), 83–95
Ivan Limonchenko, Dmitry Millionshchikov, Contemporary Mathematics, 772, Topology, Geometry, and Dynamics, 2021, 209
D. Baralic, J. Grbic, I. Limonchenko, A. Vucic, “Toric objects associated with the dodecahedron”, Filomat, 34:7 (2020), 2329–2356
T. Panov, Ya. Veryovkin, “On the commutator subgroup of a right-angled Artin group”, J. Algebra, 521 (2019), 284–298
T. Panov, S. Theriault, “The homotopy theory of polyhedral products associated with flag complexes”, Compos. Math., 155:1 (2019), 206–228
S. Dey, K. Gongopadhyay, “Commutator subgroups of twin groups and Grothendieck's cartographical groups”, J. Algebra, 530 (2019), 215–234
V. M. Buchstaber, I. Yu. Limonchenko, “Massey products, toric topology and combinatorics of polytopes”, Izv. Math., 83:6 (2019), 1081–1136
Ya. A. Veryovkin, “The Associated Lie Algebra of a Right-Angled Coxeter Group”, Proc. Steklov Inst. Math., 305 (2019), 53–62
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