On the Dimension of Cohomology of Bianchi Groups

2012/04/02 by Mehmet Haluk Şengün, Sengun, Mehmet Haluk, Seyfi Türkelli +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1204.0470

openalex publication_date 2012/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Lefschetz numbers of certain involutions, we provide lower bounds for the cuspidal cohomology of principal congruence subgroups of Bianchi groups. The asymptotic lower bounds that follow from our results complement recent results of Calegari-Emerton, Marshall and Finis-Grunewald-Tirao. Moreover, we discuss the relationship between these involutions and the base change classes in the cohomology.

Related

• Two results on Eisenstein part of homology and cohomology groups of Bianchi modular groups
• Accessing the cohomology of discrete groups above their virtual cohomological dimension
• The Integral Cohomology of the Bianchi Groups
• The mod 2 cohomology rings of congruence subgroups in the Bianchi groups
• Sharp bounds for multiplicities of Bianchi modular forms