A coarse embedding theorem for homological filling functions

2020/08/25 by Robert Kropholler, Kropholler, Robert, Mark Pengitore +1
Computer Science · Mathematics · #20E07 #20J05 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT #msc:20E07 #msc:20J05 #msc:57M07 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2008.11090

11 pages, 4 figures

openalex publication_date 2020/08/25 · arxiv created 2020/11/18 · arxiv updated 2020/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a coarse embedding into a hyperbolic group of geometric dimension 2, characterizations of finitely presentable subgroups of groups with quadratic Dehn function with geometric dimension 2, and to coarse embeddings of nilpotent groups into other nilpotent groups of the same growth and into hyperbolic groups.

Related

• Groups with no coarse embeddings into hyperbolic groups
• Quasi-isometric Higman embeddings and the Dehn function
• From the second BNSR invariant to Dehn functions of coabelian subgroups
• A Subgroup Theorem for Homological Filling Functions
• Fillings, finite generation and direct limits of relatively hyperbolic groups