Geodesic
Restricting the topology of 1–cusped arithmetic 3–manifolds
Baker, Mark D1 ; Reid, Alan W2
1IRMAR, Université de Rennes 1, 35042 Rennes, Cedex, FRANCE
2Department of Mathematics, University of Texas, 1 Station C1200, Austin, TX 78712, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1273-1298
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

This paper makes progress on classifying those closed orientable 3–manifolds M that contain knots K so that M ∖ K is arithmetic.

DOI : 10.2140/agt.2013.13.1273
Classification : 57M50, 57M25, 57M10
Keywords: arithmetic knot, cusped hyperbolic manifold, spherical orbifolds, homology $3$–spheres

Baker, Mark D  1   ; Reid, Alan W  2

1 IRMAR, Université de Rennes 1, 35042 Rennes, Cedex, FRANCE
2 Department of Mathematics, University of Texas, 1 Station C1200, Austin, TX 78712, USA 
@article{10_2140_agt_2013_13_1273,
     author = {Baker, Mark D and Reid, Alan W},
     title = {Restricting the topology of 1{\textendash}cusped arithmetic 3{\textendash}manifolds},
     journal = {Algebraic and Geometric Topology},
     pages = {1273--1298},
     year = {2013},
     volume = {13},
     number = {3},
     doi = {10.2140/agt.2013.13.1273},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1273/}
}
TY  - JOUR
AU  - Baker, Mark D
AU  - Reid, Alan W
TI  - Restricting the topology of 1–cusped arithmetic 3–manifolds
JO  - Algebraic and Geometric Topology
PY  - 2013
SP  - 1273
EP  - 1298
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1273/
DO  - 10.2140/agt.2013.13.1273
ID  - 10_2140_agt_2013_13_1273
ER  - 
%0 Journal Article
%A Baker, Mark D
%A Reid, Alan W
%T Restricting the topology of 1–cusped arithmetic 3–manifolds
%J Algebraic and Geometric Topology
%D 2013
%P 1273-1298
%V 13
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1273/
%R 10.2140/agt.2013.13.1273
%F 10_2140_agt_2013_13_1273
Baker, Mark D; Reid, Alan W. Restricting the topology of 1–cusped arithmetic 3–manifolds. Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1273-1298. doi: 10.2140/agt.2013.13.1273

[1] I Agol, Topology of hyperbolic $3$–manifolds, PhD thesis, University of California, San Diego (1998)

[2] M D Baker, A W Reid, Arithmetic knots in closed $3$–manifolds, J. Knot Theory Ramifications 11 (2002) 903

[3] W Bosma, J Cannon, C Playoust, The Magma algebra system, I, The user language, J. Symbolic Comput. 24 (1997) 235

[4] S Boyer, X Zhang, Finite Dehn surgery on knots, J. Amer. Math. Soc. 9 (1996) 1005

[5] C Cao, G R Meyerhoff, The orientable cusped hyperbolic $3$–manifolds of minimum volume, Invent. Math. 146 (2001) 451

[6] T Chinburg, D Long, A W Reid, Cusps of minimal non-compact arithmetic hyperbolic $3$–orbifolds, Pure Appl. Math. Q. 4 (2008) 1013

[7] D Coulson, O A Goodman, C D Hodgson, W D Neumann, Computing arithmetic invariants of $3$–manifolds, Experiment. Math. 9 (2000) 127

[8] M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the geometry and topology of $3$–manifolds (2011)

[9] W D Dunbar, Geometric orbifolds, Rev. Mat. Univ. Complut. Madrid 1 (1988) 67

[10] W D Dunbar, G R Meyerhoff, Volumes of hyperbolic $3$–orbifolds, Indiana Univ. Math. J. 43 (1994) 611

[11] C Frohman, B Fine, Some amalgam structures for Bianchi groups, Proc. Amer. Math. Soc. 102 (1988) 221

[12] C M Gordon, Dehn filling: a survey, from: "Knot theory" (editors V F R Jones, J Kania-Bartoszyńska, J H Przytycki, V G Traczyk Pawełand Turaev), Banach Center Publ. 42, Polish Acad. Sci. Inst. Math., Warsaw (1998) 129

[13] F Grunewald, J Schwermer, Subgroups of Bianchi groups and arithmetic quotients of hyperbolic $3$–space, Trans. Amer. Math. Soc. 335 (1993) 47

[14] M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243

[15] C Maclachlan, A W Reid, The arithmetic of hyperbolic $3$–manifolds, Graduate Texts in Mathematics 219, Springer (2003)

[16] M Newman, Integral matrices, Pure and Applied Mathematics 45, Academic Press (1972)

[17] A W Reid, Arithmeticity of knot complements, J. London Math. Soc. 43 (1991) 171

[18] R G Swan, Generators and relations for certain special linear groups, Advances in Math. 6 (1971) 1

Cité par Sources :