Abstract:
We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of graph products. By way of application, we describe the restricted Lie algebra associated with the lower $2$-central series of a right-angled Coxeter group and identify its universal enveloping algebra with the loop homology of the Davis–Januszkiewicz space.
The work of Taras Panov (Sections 2, 3 and 7) was supported by the Russian Science Foundation under grant no. 23-11-00143, http://rscf.ru/en/project/23-11-00143/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences. The work of Temurbek Rakhmatullaev (Sections 4-6) was as carried out within the project “Mirror Laboratories” of HSE University, Russian Federation.
Citation:
T. E. Panov, T. A. Rahmatullaev, “Polyhedral products, graph products and $p$-central series”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 293–310
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