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The homeomorphism problem for closed $3$–manifolds

Peter Scott and Hamish Short

Algebraic & Geometric Topology 14 (2014) 2431–2444
Bibliography
1 J M Alonso, T Brady, D Cooper, V Ferlini, M Lustig, M Mihalik, M Shapiro, H Short, Notes on word hyperbolic groups, from: "Group theory from a geometrical viewpoint" (editor H Short), World Sci. Publ. (1991) 3 MR1170363
2 T Becker, V Weispfenning, Gröbner bases: A computational approach to commutative algebra, Graduate Texts in Math. 141, Springer (1993) MR1213453
3 L Bessières, G Besson, S Maillot, M Boileau, J Porti, Geometrisation of $3$–manifolds, EMS Tracts in Math. 13, European Math. Soc. (EMS), Zürich (2010) MR2683385
4 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer, Berlin (1999) MR1744486
5 A L Edmonds, J H Ewing, R S Kulkarni, Torsion free subgroups of Fuchsian groups and tessellations of surfaces, Bull. Amer. Math. Soc. 6 (1982) 456 MR648534
6 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
7 S M Gersten, H B Short, Rational subgroups of biautomatic groups, Ann. of Math. 134 (1991) 125 MR1114609
8 S M Gersten, H Short, Small cancellation theory and automatic groups, II, Invent. Math. 105 (1991) 641 MR1117155
9 J E Hopcroft, J D Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley Publishing Co. (1979) MR645539
10 W Jaco, Peking summer school lectures, preprint (2005)
11 W Jaco, U Oertel, An algorithm to decide if a $3$–manifold is a Haken manifold, Topology 23 (1984) 195 MR744850
12 W Jaco, J L Tollefson, Algorithms for the complete decomposition of a closed $3$–manifold, Illinois J. Math. 39 (1995) 358 MR1339832
13 R Loos, Computing in algebraic extensions, from: "Computer algebra" (editors B Buchberger, G E Collins, R Loos, R Albrecht), Springer, Vienna (1983) 173 MR728972
14 J Manning, Algorithmic detection and description of hyperbolic structures on closed $3$–manifolds with solvable word problem, Geom. Topol. 6 (2002) 1 MR1885587
15 S Matveev, Algorithmic topology and classification of 3-manifolds, Algorithms and Computation in Math. 9, Springer, Berlin (2007) MR2341532
16 P Papasoglu, An algorithm detecting hyperbolicity, from: "Geometric and computational perspectives on infinite groups" (editors G Baumslag, D Epstein, R Gilman, H Short, C Sims), DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Amer. Math. Soc. (1996) 193 MR1364185
17 G Perelman, The entropy formula for the Ricci flow and its geometric applications, (2002) arXiv:math/0211159
18 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain $3$–manifolds, (2002) arXiv:math/0307245
19 G Perelman, Ricci flow with surgery on $3$–manifolds, (2002) arXiv:math/0303109
20 J H Rubinstein, An algorithm to recognize the $3$–sphere, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2" (editor S D Chatterji), Birkhäuser, Basel (1995) 601 MR1403961
21 P Scott, The geometries of $3$–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
22 Z Sela, The isomorphism problem for hyperbolic groups, I, Ann. of Math. 141 (1995) 217 MR1324134
23 A Thompson, Thin position and the recognition problem for $S^3$, Math. Res. Lett. 1 (1994) 613 MR1295555