[Complexes de groupes et petite simplification géométrique sur les graphes de groupes]
We explain and generalize a construction due to Gromov to realize geometric small cancelation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that the hyperbolicity and some finiteness properties of the small cancelation quotient can be deduced from analogous properties for the local groups of the initial graph of groups.
Nous généralisons une construction de Gromov afin de réaliser certains groupes à petite simplification géométrique sur un graphe de groupes comme groupes fondamentaux de complexes de groupes de dimension à courbure négative ou nulle. Nous donnons ensuite des conditions pour que l’hyperbolicité et certaines propriétés de finitude de tels groupes se déduisent des propriétés analogues pour les groupes locaux du graphe de groupes initial.
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DOI : 10.24033/bsmf.2734
Keywords: Geometric small cancelation, complexes of groups, hyperbolic groups, classifying spaces.
Mots-clés : Petite simplification géométrique, complexes de groupes, groupes hyperboliques, espaces classifiants.
Martin, Alexandre 1
@article{BSMF_2017__145_2_193_0,
author = {Martin, Alexandre},
title = {Complexes of groups and geometric small cancelation over graphs of groups},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {193--223},
year = {2017},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {145},
number = {2},
doi = {10.24033/bsmf.2734},
mrnumber = {3749783},
zbl = {1446.20066},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2734/}
}
TY - JOUR AU - Martin, Alexandre TI - Complexes of groups and geometric small cancelation over graphs of groups JO - Bulletin de la Société Mathématique de France PY - 2017 SP - 193 EP - 223 VL - 145 IS - 2 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2734/ DO - 10.24033/bsmf.2734 LA - en ID - BSMF_2017__145_2_193_0 ER -
%0 Journal Article %A Martin, Alexandre %T Complexes of groups and geometric small cancelation over graphs of groups %J Bulletin de la Société Mathématique de France %D 2017 %P 193-223 %V 145 %N 2 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2734/ %R 10.24033/bsmf.2734 %G en %F BSMF_2017__145_2_193_0
Martin, Alexandre. Complexes of groups and geometric small cancelation over graphs of groups. Bulletin de la Société Mathématique de France, Tome 145 (2017) no. 2, pp. 193-223. doi: 10.24033/bsmf.2734
Geometry of infinitely presented small cancellation groups, rapid decay and quasi-homomorphisms | arXiv
Infinitely presented small cancellation groups have Haagerup property | arXiv
A combination theorem for negatively curved groups, J. Differential Geom., Volume 35 (1992), pp. 85-101 http://projecteuclid.org/... | MR | Zbl
Metric spaces of non-positive curvature, Grundl. math. Wiss., 319, Springer, 1999, 643 pages | MR | Zbl | DOI
Geodesics and curvature in metric simplicial complexes, Group theory from a geometrical viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, pp. 373-463 | MR | Zbl
Petite simplification dans les groupes hyperboliques, Ann. Fac. Sci. Toulouse Math., Volume 3 (1994), pp. 161-221 | Numdam | MR | Zbl | DOI
Complexes of groups, Proc. London Math. Soc., Volume 65 (1992), pp. 199-224 | MR | Zbl | DOI
Asphericity and small cancellation theory for rotation families of groups, Groups Geom. Dyn., Volume 5 (2011), pp. 729-765 | MR | Zbl | DOI
Sous-groupes distingués et quotients des groupes hyperboliques, Duke Math. J., Volume 83 (1996), pp. 661-682 | MR | Zbl | DOI
Courbure mésoscopique et théorie de la toute petite simplification, J. Topol., Volume 1 (2008), pp. 804-836 | MR | Zbl | DOI
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces | arXiv
-spaces: construction and concentration, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), Volume 280 (2001), p. 100-140, 299–300 | MR | Zbl | DOI
Random walk in random groups, Geom. Funct. Anal., Volume 13 (2003), pp. 73-146 | MR | Zbl | DOI
Complexes of groups and orbihedra, Group theory from a geometrical viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, pp. 504-540 | MR | Zbl
Extension of complexes of groups, Ann. Inst. Fourier (Grenoble), Volume 42 (1992), pp. 275-311 | Numdam | MR | Zbl | DOI
Combinatorial group theory, Classics in Mathematics, Springer, 2001, 339 pages | MR | Zbl | DOI
Combination of classifying spaces for proper actions | arXiv
Non-positively curved complexes of groups and boundaries, Geom. Topol., Volume 18 (2014), pp. 31-102 | MR | Zbl | DOI
Fans and ladders in small cancellation theory, Proc. London Math. Soc., Volume 84 (2002), pp. 599-644 | MR | Zbl | DOI
Geometry of defining relations in groups, Mathematics and its Applications (Soviet Series), 70, Kluwer Academic Publishers Group, Dordrecht, 1991, 505 pages | MR | Zbl | DOI
On residualing homomorphisms and -subgroups of hyperbolic groups, Internat. J. Algebra Comput., Volume 3 (1993), pp. 365-409 | MR | Zbl | DOI
Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc., Volume 71 (1995), pp. 585-617 | MR | Zbl | DOI
Arbres, amalgames, , Astérisque, 46, Soc. Math. France, 1977, 189 pp. (1 plate) pages | Zbl | Numdam | MR
Non-positively curved triangles of groups, Group theory from a geometrical viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, pp. 491-503 | MR | Zbl
Cubulating small cancellation groups, Geom. Funct. Anal., Volume 14 (2004), pp. 150-214 | MR | Zbl | DOI
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