Fractional isoperimetric inequalities and subgroup distortion

@article{Bridson1996FractionalII,
  title={Fractional isoperimetric inequalities and subgroup distortion},
  author={Martin R. Bridson},
  journal={Journal of the American Mathematical Society},
  year={1996},
  volume={12},
  pages={1103-1118}
}
  • M. Bridson
  • Published 20 December 1996
  • Mathematics
  • Journal of the American Mathematical Society
Isoperimetric inequalities measure the complexity of the word problem in finitely presented groups by giving a bound on the number of relators that one must apply in order to show that a word w in the given generators represents the identity. Such bounds are given in terms of the length of w, and the function describing the optimal bound is known as the Dehn function of the group. (Modulo a standard equivalence relation _, the Dehn function is an invariant of the group, not just the given… 

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References

SHOWING 1-10 OF 40 REFERENCES
Isoperimetric inequalities and the homology of groups
An isoperimetric function for a finitely presented group G bounds the number of defining relations needed to prove that a word w =G 1 in terms of the length of w. Suppose G = F/R is a finitely
Isoperimetric and isodiametric functions of groups
This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. In particular, we show how to construct a finitely presented group with
Isoperimetric inequalities for the fundamental groups of torus bundles over the circle
We give upper bounds for isoperimetric functions of semi-direct products in terms of the asymptotic behaviour of ||Ak|| ask → ∞. In the caseA ∈ Sp(n, ℤ) we show that these bounds are sharp. This
Combinatorial Group Theory
Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.
On the geometry of normal forms in discrete groups
We study normal forms in finitely generated groups from the geometric viewpoint of combings. We introduce notions of combability considerably weaker than those commonly in use. We prove that groups
Combings of semidirect products and 3-manifold groups
IfG is a finitely generated group that is abelian or word-hyperbolic andH is an asynchronously combable group then every split extension ofG byH is asynchronously combable. The fundamental group of
Casson's Idea about 3-Manifolds whose Universal Cover is R3
TLDR
If the fundamental group of a closed aspherical 3-manifold has some presentation which satisfies C2 or , then its universal cover is simply connected at infinity.
Hyperbolicity of Groups with Subquadratic isoperimetric inequality
The author gives a simple and coherent proof of Gromov's statement on hyperbolicity of groups with subquadratic isoperimetric inequality.
Geometric Group Theory: Proceedings of a Special Research Quarter at The Ohio State University, Spring 1992
Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of
Geometric Group Theory: Isoperimetric and Isodiametric Functions of Finite Presentations
We survey current work relating to isoperimetric functions and isodiametric functions of finite presentations. §
...
...