Authors: Baralić, Đorđe 
Vavpetič, Aleš
Vučić, Aleksandar
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Universal Complexes in Toric Topology
Journal: Results in Mathematics
Volume: 78
First page: 218
Issue Date: 2023
Rank: ~M21a
ISSN: 1422-6383
DOI: 10.1007/s00025-023-01995-3
We study combinatorial and topological properties of the universal complexes X(Fpn) and K(Fpn) whose simplices are certain unimodular subsets of Fpn . We calculate their f -vectors and the bigraded Betti numbers of their Tor-algebras, show that they are shellable, and find their applications in toric topology and number theory. We show that the Lusternick–Schnirelmann category of the moment angle complex of X(Fpn) is n, provided p is an odd prime, and the Lusternick–Schnirelmann category of the moment angle complex of K(Fpn) is [n2] . Based on the universal complexes, we introduce the Buchstaber invariant sp for a prime number p.
Keywords: bigraded Betti numbers | Lusternik–Schnirelmann category | moment-angle complex | Tor-algebra | Universal complexes
Publisher: Springer Link
Project: Research on this paper was partially supported by the bilateral project “Discrete Morse theory and its Applications” funded by the Ministry for Education and Science of the Republic of Serbia and the Ministry of Education, Science and Sport of the Republic of Slovenia.

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