Geodesic
Counting immersed surfaces in hyperbolic 3–manifolds
Masters, Joseph D1
1Mathematics Department, Rice University, Houston TX 77005, USA, Mathematics Department, SUNY Buffalo, Buffalo NY 14260, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 835-864
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We count the number of conjugacy classes of maximal, genus g, surface subroups in hyperbolic 3–manifold groups. For any closed hyperbolic 3–manifold, we show that there is an upper bound on this number which grows factorially with g. We also give a class of closed hyperbolic 3–manifolds for which there is a lower bound of the same type.

DOI : 10.2140/agt.2005.5.835
Keywords: surface subgroups, bending, pleated surfaces, reflection orbifolds

Masters, Joseph D  1

1 Mathematics Department, Rice University, Houston TX 77005, USA, Mathematics Department, SUNY Buffalo, Buffalo NY 14260, USA 
@article{10_2140_agt_2005_5_835,
     author = {Masters, Joseph D},
     title = {Counting immersed surfaces in hyperbolic 3{\textendash}manifolds},
     journal = {Algebraic and Geometric Topology},
     pages = {835--864},
     year = {2005},
     volume = {5},
     number = {2},
     doi = {10.2140/agt.2005.5.835},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.835/}
}
TY  - JOUR
AU  - Masters, Joseph D
TI  - Counting immersed surfaces in hyperbolic 3–manifolds
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 835
EP  - 864
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.835/
DO  - 10.2140/agt.2005.5.835
ID  - 10_2140_agt_2005_5_835
ER  - 
%0 Journal Article
%A Masters, Joseph D
%T Counting immersed surfaces in hyperbolic 3–manifolds
%J Algebraic and Geometric Topology
%D 2005
%P 835-864
%V 5
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.835/
%R 10.2140/agt.2005.5.835
%F 10_2140_agt_2005_5_835
Masters, Joseph D. Counting immersed surfaces in hyperbolic 3–manifolds. Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 835-864. doi: 10.2140/agt.2005.5.835

[1] B H Bowditch, G Mess, A 4–dimensional Kleinian group, Trans. Amer. Math. Soc. 344 (1994) 391

[2] J Elstrodt, F Grunewald, J Mennicke, Groups acting on hyperbolic space, Springer Monographs in Mathematics, Springer (1998)

[3] D G James, C Maclachlan, Fuchsian subgroups of Bianchi groups, Trans. Amer. Math. Soc. 348 (1996) 1989

[4] A Lubotzky, Counting finite index subgroups, from: "Groups '93 Galway/St. Andrews, Vol. 2", London Math. Soc. Lecture Note Ser. 212, Cambridge Univ. Press (1995) 368

[5] C Maclachlan, A W Reid, Parametrizing Fuchsian subgroups of the Bianchi groups, Canad. J. Math. 43 (1991) 158

[6] T Soma, Virtual fibers in hyperbolic 3–manifolds, Topology Appl. 41 (1991) 179

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

[8] W P Thurston, The geometry and topology of three-manifolds, lecture notes, Princeton University (1978–1980)

Cité par Sources :