2014/09/12 by Alexandre Martin, Martin, Alexandre, Markus Steenbock +1
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.1409.3678
46 pages, 8 figures
openalex publication_date 2014/09/12 · arxiv created 2015/12/23 · arxiv updated 2015/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a group obtained as a quotient of the free product of finitely many cubulable groups by a finite set of relators satisfying the classical C'(1/6)--small cancellation condition is cubulable. This yields a new large class of relatively hyperbolic groups that can be cubulated, and constitutes the first instance of a cubulability theorem for relatively hyperbolic groups which does not require any geometric assumption on the peripheral subgroups besides their cubulability. We do this by constructing appropriate wallspace structures for such groups, by combining walls of the free factors with walls coming from the universal cover of an associated 2-complex of groups.