Volume 6, issue 1 (2002)

Download this article
For printing
Recent Issues

Volume 29
Issue 7, 3345–3919
Issue 6, 2783–3343
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Algorithmic detection and description of hyperbolic structures on closed 3–manifolds with solvable word problem

Jason Fox Manning

Geometry & Topology 6 (2002) 1–26
Bibliography
1 W Ballmann, M Gromov, V Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics 61, Birkhäuser (1985) MR823981
2 A F Beardon, The geometry of discrete groups, Graduate Texts in Mathematics 91, Springer (1983) MR698777
3 T Becker, V Weispfenning, Gröbner bases, Graduate Texts in Mathematics 141, Springer (1993) MR1213453
4 R H Bing, Locally tame sets are tame, Ann. of Math. $(2)$ 59 (1954) 145 MR0061377
5 D Cooper, C D Hodgson, S P Kerckhoff, Thurston's Orbifold Theorem, to appear
6 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. $(2)$ 117 (1983) 109 MR683804
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) MR1161694
8 D Gabai, G R Meyerhoff, N Thurston, Homotopy hyperbolic 3–manifolds are hyperbolic, Ann. of Math. $(2)$ 157 (2003) 335 MR1973051
9 G Hemion, On the classification of homeomorphisms of 2–manifolds and the classification of 3–manifolds, Acta Math. 142 (1979) 123 MR512214
10 W Jaco, J L Tollefson, Algorithms for the complete decomposition of a closed 3–manifold, Illinois J. Math. 39 (1995) 358 MR1339832
11 M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
12 R Loos, Computing in algebraic extensions, from: "Computer algebra", Springer (1983) 173 MR728972
13 B Maskit, On Poincaré's theorem for fundamental polygons, Advances in Math. 7 (1971) 219 MR0297997
14 K Matsuzaki, M Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1998) MR1638795
15 E E Moise, Affine structures in 3–manifolds V: The triangulation theorem and Hauptvermutung, Ann. of Math. $(2)$ 56 (1952) 96 MR0048805
16 G A Niblo, L D Reeves, The geometry of cube complexes and the complexity of their fundamental groups, Topology 37 (1998) 621 MR1604899
17 C Petronio, J R Weeks, Partially flat ideal triangulations of cusped hyperbolic 3–manifolds, Osaka J. Math. 37 (2000) 453 MR1772844
18 R Riley, Applications of a computer implementation of Poincaré's theorem on fundamental polyhedra, Math. Comp. 40 (1983) 607 MR689477
19 J H Rubinstein, An algorithm to recognize the 3–sphere, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)", Birkhäuser (1995) 601 MR1403961
20 P Scott, The geometries of 3–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
21 H Seifert, Komplexe mit Seitenzuordnung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1975) 49 MR0383219
22 Z Sela, Topics in 3–manifolds, PhD thesis, Hebrew University (1991)
23 Z Sela, The isomorphism problem for hyperbolic groups I, Ann. of Math. $(2)$ 141 (1995) 217 MR1324134
24 A Skinner, The word problem in a class of non–Haken 3–manifolds, Topology 33 (1994) 215 MR1273783
25 M Stocking, Almost normal surfaces in 3–manifolds, PhD thesis, UC Davis (1996)
26 A Thompson, Thin position and the recognition problem for $S^3$, Math. Res. Lett. 1 (1994) 613 MR1295555
27 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. $($N.S.$)$ 6 (1982) 357 MR648524
28 F Waldhausen, The word problem in fundamental groups of sufficiently large irreducible 3–manifolds, Ann. of Math. $(2)$ 88 (1968) 272 MR0240822
29 F Waldhausen, Recent results on sufficiently large 3–manifolds, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 21 MR520520