Lδ groups are almost convex and have a sub-cubic Dehn function
Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 23-29
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We prove that if the Cayley graph of a finitely generated group enjoys the property Lδ then the group is almost convex and has a sub-cubic isoperimetric function.

DOI : 10.2140/agt.2004.4.23
Keywords: almost convex, isoperimetric function, property $L_\delta$

Elder, Murray  1

1 School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland
@article{10_2140_agt_2004_4_23,
     author = {Elder, Murray},
     title = {L\ensuremath{\delta} groups are almost convex and have a sub-cubic {Dehn} function},
     journal = {Algebraic and Geometric Topology},
     pages = {23--29},
     year = {2004},
     volume = {4},
     number = {1},
     doi = {10.2140/agt.2004.4.23},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2004.4.23/}
}
TY  - JOUR
AU  - Elder, Murray
TI  - Lδ groups are almost convex and have a sub-cubic Dehn function
JO  - Algebraic and Geometric Topology
PY  - 2004
SP  - 23
EP  - 29
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2004.4.23/
DO  - 10.2140/agt.2004.4.23
ID  - 10_2140_agt_2004_4_23
ER  - 
%0 Journal Article
%A Elder, Murray
%T Lδ groups are almost convex and have a sub-cubic Dehn function
%J Algebraic and Geometric Topology
%D 2004
%P 23-29
%V 4
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2004.4.23/
%R 10.2140/agt.2004.4.23
%F 10_2140_agt_2004_4_23
Elder, Murray. Lδ groups are almost convex and have a sub-cubic Dehn function. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 23-29. doi: 10.2140/agt.2004.4.23

[1] B H Bowditch, A short proof that a subquadratic isoperimetric inequality implies a linear one, Michigan Math. J. 42 (1995) 103

[2] N Brady, M R Bridson, There is only one gap in the isoperimetric spectrum, Geom. Funct. Anal. 10 (2000) 1053

[3] M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, Springer (1999)

[4] J W Cannon, Almost convex groups, Geom. Dedicata 22 (1987) 197

[5] I Chatterji, K Ruane, Some geometric groups with rapid decay, Geom. Funct. Anal. 15 (2005) 311

[6] D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett Publishers (1992)

[7] S M Gersten, Introduction to hyperbolic and automatic groups, from: "Summer School in Group Theory in Banff, 1996", CRM Proc. Lecture Notes 17, Amer. Math. Soc. (1999) 45

[8] W D Neumann, M Shapiro, Geometric Group Theory: Notes for the ANU Workshop January/February 1996, Topology Atlas document iaai-13

[9] A Y Ol’Shanskiĭ, Hyperbolicity of groups with subquadratic isoperimetric inequality, Internat. J. Algebra Comput. 1 (1991) 281

[10] C Thiel, Zur fast–Konvexität einiger nilpotenter Gruppen, Bonner Mathematische Schriften 234, Universität Bonn Mathematisches Institut (1992) 50

Cité par Sources :