2010/09/06 by Kęstutis Česnavičius, Kestutis Cesnavicius, Cesnavicius, Kestutis
Computer Science · Mathematics · #05E45 #20F55 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:05E45 #msc:20F55
paper · pdf · doi:10.48550/arxiv.1009.1106
14 pages, 10 figures
arxiv created 2010/09/06 · openalex publication_date 2010/09/06 · arxiv updated 2010/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Flag Complex Conjecture of Charney and Davis states that for a simplicial complex S which triangulates a (2n - 1)-generalized homology sphere as a flag complex one has (-1)n ∑σ∈ S ((-1)/(2))dimσ+ 1 ≥ 0, where the sum runs over all simplices σ of S (including the empty simplex). Interpreting the 1-skeleta of σ∈ S as graphs of Coxeter groups, we present a stronger version of this conjecture, and prove the equivalence of the latter to the Flag Complex Conjecture.