Geodesic
Splittings and C–complexes
Mj, Mahan1 ; Scott, Peter2 ; Swarup, Gadde3
1Department of Mathematics, RKM Vivekananda University, Belur Math, WB-711 202, India
2Mathematics Department, University of Michigan, Ann Arbor, Michigan 48109, USA
3718, High Street Road, Glen Waverley, Victoria 3150, Australia
Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 1971-1986
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

The intersection pattern of the translates of the limit set of a quasi-convex subgroup of a hyperbolic group can be coded in a natural incidence graph, which suggests connections with the splittings of the ambient group. A similar incidence graph exists for any subgroup of a group. We show that the disconnectedness of this graph for codimension one subgroups leads to splittings. We also reprove some results of Peter Kropholler on splittings of groups over malnormal subgroups and variants of them.

DOI : 10.2140/agt.2009.9.1971
Keywords: splittings of groups, C–complexes, quasiconvex, codimension one subgroup

Mj, Mahan  1   ; Scott, Peter  2   ; Swarup, Gadde  3

1 Department of Mathematics, RKM Vivekananda University, Belur Math, WB-711 202, India
2 Mathematics Department, University of Michigan, Ann Arbor, Michigan 48109, USA
3 718, High Street Road, Glen Waverley, Victoria 3150, Australia 
@article{10_2140_agt_2009_9_1971,
     author = {Mj, Mahan and Scott, Peter and Swarup, Gadde},
     title = {Splittings and {C{\textendash}complexes}},
     journal = {Algebraic and Geometric Topology},
     pages = {1971--1986},
     year = {2009},
     volume = {9},
     number = {4},
     doi = {10.2140/agt.2009.9.1971},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1971/}
}
TY  - JOUR
AU  - Mj, Mahan
AU  - Scott, Peter
AU  - Swarup, Gadde
TI  - Splittings and C–complexes
JO  - Algebraic and Geometric Topology
PY  - 2009
SP  - 1971
EP  - 1986
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1971/
DO  - 10.2140/agt.2009.9.1971
ID  - 10_2140_agt_2009_9_1971
ER  - 
%0 Journal Article
%A Mj, Mahan
%A Scott, Peter
%A Swarup, Gadde
%T Splittings and C–complexes
%J Algebraic and Geometric Topology
%D 2009
%P 1971-1986
%V 9
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1971/
%R 10.2140/agt.2009.9.1971
%F 10_2140_agt_2009_9_1971
Mj, Mahan; Scott, Peter; Swarup, Gadde. Splittings and C–complexes. Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 1971-1986. doi: 10.2140/agt.2009.9.1971

[1] B H Bowditch, Splittings of finitely generated groups over two-ended subgroups, Trans. Amer. Math. Soc. 354 (2002) 1049

[2] D E Cohen, Groups of cohomological dimension one, 245, Springer (1972)

[3] M J Dunwoody, Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. (3) 38 (1979) 193

[4] R Gitik, M Mitra, E Rips, M Sageev, Widths of subgroups, Trans. Amer. Math. Soc. 350 (1998) 321

[5] P H Kropholler, A group-theoretic proof of the torus theorem, from: "Geometric group theory, Vol. 1 (Sussex, 1991)", London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 138

[6] P H Kropholler, M A Roller, Relative ends and duality groups, J. Pure Appl. Algebra 61 (1989) 197

[7] M Mitra, Height in splittings of hyperbolic groups, Proc. Indian Acad. Sci. Math. Sci. 114 (2004) 39

[8] M Mj, Relative rigidity, quasiconvexity and C–complexes, Algebr. Geom. Topol. 8 (2008) 1691

[9] G A Niblo, The singularity obstruction for group splittings, Topology Appl. 119 (2002) 17

[10] G Niblo, M Sageev, P Scott, G A Swarup, Minimal cubings, Internat. J. Algebra Comput. 15 (2005) 343

[11] M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. (3) 71 (1995) 585

[12] P Scott, The symmetry of intersection numbers in group theory, Geom. Topol. 2 (1998) 11

[13] P Scott, G A Swarup, Regular neighbourhoods and canonical decompositions for groups, Astérisque (2003)

Cité par Sources :