Geodesic
Combing Euclidean buildings
Noskov, Gennady A1
1 IITAM SORAN, Pevtsova 13, Omsk 644099, Russia
Geometry & topology, Tome 4 (2000) no. 1, pp. 85-116.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

For an arbitrary Euclidean building we define a certain combing, which satisfies the “fellow traveller property” and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order preserving automorphisms on a Euclidean building of one of the types An,Bn,Cn admits a biautomatic structure.

DOI : 10.2140/gt.2000.4.85
Keywords: Euclidean building, automatic group, combing

Noskov, Gennady A 1

1 IITAM SORAN, Pevtsova 13, Omsk 644099, Russia 
@article{GT_2000_4_1_a1,
     author = {Noskov, Gennady A},
     title = {Combing {Euclidean} buildings},
     journal = {Geometry & topology},
     pages = {85--116},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2000},
     doi = {10.2140/gt.2000.4.85},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2000.4.85/}
}
TY  - JOUR
AU  - Noskov, Gennady A
TI  - Combing Euclidean buildings
JO  - Geometry & topology
PY  - 2000
SP  - 85
EP  - 116
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2000.4.85/
DO  - 10.2140/gt.2000.4.85
ID  - GT_2000_4_1_a1
ER  - 
%0 Journal Article
%A Noskov, Gennady A
%T Combing Euclidean buildings
%J Geometry & topology
%D 2000
%P 85-116
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2000.4.85/
%R 10.2140/gt.2000.4.85
%F GT_2000_4_1_a1
Noskov, Gennady A. Combing Euclidean buildings. Geometry & topology, Tome 4 (2000) no. 1, pp. 85-116. doi : 10.2140/gt.2000.4.85. http://geodesic.mathdoc.fr/articles/10.2140/gt.2000.4.85/

[1] W Ballmann, M Brin, Polygonal complexes and combinatorial group theory, Geom. Dedicata 50 (1994) 165

[2] N Bourbaki, Groupes et algèbres de Lie: Chapitres IV, V et VI, Hermann (1972) 320

[3] M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften 319, Springer (1999)

[4] M R Bridson, Geodesics and curvature in metric simplicial complexes, from: "Group theory from a geometrical viewpoint (Trieste, 1990)", World Sci. Publ., River Edge, NJ (1991) 373

[5] K S Brown, Buildings, Springer Monographs in Mathematics, Springer (1998)

[6] D I Cartwright, M Shapiro, Hyperbolic buildings, affine buildings, and automatic groups, Michigan Math. J. 42 (1995) 511

[7] 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)

[8] S M Gersten, H B Short, Small cancellation theory and automatic groups, Invent. Math. 102 (1990) 305

[9] S M Gersten, H Short, Small cancellation theory and automatic groups II, Invent. Math. 105 (1991) 641

[10] J E Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press (1990)

[11] W D Neumann, M Shapiro, Automatic structures and boundaries for graphs of groups, Internat. J. Algebra Comput. 4 (1994) 591

[12] G A Niblo, L D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621

[13] G A Noskov, Bicombing of triangular buildings, Sibirsk. Mat. Zh. 40 (1999) 1109

Cité par Sources :