Geodesic
Engulfing in word-hyperbolic groups
Niblo, Graham A1 ; Williams, Ben T1
1Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, UK
Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 743-755
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We examine residual properties of word-hyperbolic groups, adapting a method introduced by Darren Long to study the residual properties of Kleinian groups.

DOI : 10.2140/agt.2002.2.743
Keywords: word hyperbolic groups, residual finiteness, engulfing

Niblo, Graham A  1   ; Williams, Ben T  1

1 Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, UK 
@article{10_2140_agt_2002_2_743,
     author = {Niblo, Graham A and Williams, Ben T},
     title = {Engulfing in word-hyperbolic groups},
     journal = {Algebraic and Geometric Topology},
     pages = {743--755},
     year = {2002},
     volume = {2},
     number = {2},
     doi = {10.2140/agt.2002.2.743},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.743/}
}
TY  - JOUR
AU  - Niblo, Graham A
AU  - Williams, Ben T
TI  - Engulfing in word-hyperbolic groups
JO  - Algebraic and Geometric Topology
PY  - 2002
SP  - 743
EP  - 755
VL  - 2
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.743/
DO  - 10.2140/agt.2002.2.743
ID  - 10_2140_agt_2002_2_743
ER  - 
%0 Journal Article
%A Niblo, Graham A
%A Williams, Ben T
%T Engulfing in word-hyperbolic groups
%J Algebraic and Geometric Topology
%D 2002
%P 743-755
%V 2
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.743/
%R 10.2140/agt.2002.2.743
%F 10_2140_agt_2002_2_743
Niblo, Graham A; Williams, Ben T. Engulfing in word-hyperbolic groups. Algebraic and Geometric Topology, Tome 2 (2002) no. 2, pp. 743-755. doi: 10.2140/agt.2002.2.743

[1] I Agol, D D Long, A W Reid, The Bianchi groups are separable on geometrically finite subgroups, Ann. of Math. $(2)$ 153 (2001) 599

[2] R G Burns, A Karrass, D Solitar, A note on groups with separable finitely generated subgroups, Bull. Austral. Math. Soc. 36 (1987) 153

[3] , Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics 83, Birkhäuser (1990)

[4] R Gitik, Doubles of groups and hyperbolic LERF 3–manifolds, Ann. of Math. $(2)$ 150 (1999) 775

[5] M Hall Jr., Coset representations in free groups, Trans. Amer. Math. Soc. 67 (1949) 421

[6] I Kapovich, H Short, Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups, Canad. J. Math. 48 (1996) 1224

[7] I Kapovich, D T Wise, The equivalence of some residual properties of word-hyperbolic groups, J. Algebra 223 (2000) 562

[8] D D Long, Engulfing and subgroup separability for hyperbolic groups, Trans. Amer. Math. Soc. 308 (1988) 849

[9] D D Long, G A Niblo, Subgroup separability and 3–manifold groups, Math. Z. 207 (1991) 209

[10] D D Long, A W Reid, The fundamental group of the double of the figure-eight knot exterior is GFERF, Bull. London Math. Soc. 33 (2001) 391

[11] L M Lopez, Residual finiteness of surface groups via tessellations, Discrete Comput. Geom. 11 (1994) 201

[12] G A Niblo, D T Wise, The engulfing property for 3–manifolds, from: "The Epstein birthday schrift", Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry (1998) 413

[13] P Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. $(2)$ 17 (1978) 555

[14] B T Williams, Two topics in geometric group theory, PhD thesis, University of Southampton (1998)

[15] D T Wise, Subgroup separability of the figure 8 knot group, Topology 45 (2006) 421

Cité par Sources :