Polynomially-bounded Dehn functions of groups

  • Alexander Yu. Olshanskii

    Vanderbilt University, Nashville, USA, and Moscow State University, Russia


It is well known that every subqadratic Dehn function is linear. A question by Bridson asked to describe the isoperimetric spectrum of groups, that is the set of all numbers such that is equivalent to the Dehn function of a finitely presented group. The goal of this paper is to give a description of the isoperimetric spectrum. Earlier a similar description was given by Sapir, Birget and Rips for the intersection of the isoperimetric spectrum with . Lowering the bound from 4 to 2 required significant new ideas and tools.

Cite this article

Alexander Yu. Olshanskii, Polynomially-bounded Dehn functions of groups. J. Comb. Algebra 2 (2018), no. 4, pp. 311–433

DOI 10.4171/JCA/2-4-1