On finite arithmetic simplicial complexes

2010/06/16 by Mihran Papikian, Papikian, Mihran
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Topological and Geometric Data Analysis #math.NT

paper · pdf · doi:10.48550/arxiv.1006.3198

14 pages

arxiv created 2010/06/16 · openalex publication_date 2010/06/16 · arxiv updated 2010/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Euler-Poincaré characteristic of quotients of the Bruhat-Tits building of PGL(n) under the action of arithmetic groups arising from central division algebras over rational function fields of positive characteristic. We use this result to determine the structure of the quotient simplicial complex in certain cases.

Related

• The extremal symmetry of arithmetic simplicial complexes
• Quotients of trees for arithmetic subgroups of PGL2 over a rational function field
• Arithmetic quotients of the Bruhat-Tits building for projective general linear group in positive characteristic
• Vector Bundles and Arithmetical Groups I. The higher Bruhat-Tits tree
• Explicit Constructions of Ramanujan Complexes of Type A_d