1 |
S I Adyan,
Finitely presented groups and algorithms, Dokl. Akad.
Nauk SSSR 117 (1957) 9 MR0095873 |
2 |
S I Adyan,
Unsolvability of some algorithmic problems in the theory of
groups, Trudy Moskov. Mat. Obšč. 6 (1957) 231 MR0095872 |
3 |
I Agol, Tameness of
hyperbolic 3–manifolds,
preprint (2004) arXiv:math/0405568 |
4 |
I Agol, Criteria for virtual
fibering, J. Topol. 1 (2008) 269 MR2399130 |
5 |
I Agol, The virtual
Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553 |
6 |
I Agol, J Hass,
W Thurston, The
computational complexity of knot genus and spanning
area, Trans. Amer. Math. Soc. 358 (2006) 3821 MR2219001 |
7 |
M Aschenbrenner, S
Friedl,
3–manifold groups are virtually residually p, 1058, Amer. Math. Soc. (2013)
MR3100378 |
8 |
M Aschenbrenner, S
Friedl, H Wilton, 3–manifold groups, 20, Euro. Math. Soc.
(2015) |
9 |
G Baumslag, D
Solitar, Some
two-generator one-relator non-Hopfian groups, Bull.
Amer. Math. Soc. 68 (1962) 199 MR0142635 |
10 |
I Belegradek,
Topology of open nonpositively curved manifolds,
preprint (2014) arXiv:1306.1256 |
11 |
L Bessières, G
Besson, M Boileau, S Maillot, J Porti,
Geometrisation of 3–manifolds, 13, Euro. Math. Soc.
(2010) |
12 |
F Bonahon,
Geometric structures on 3–manifolds, from: "Handbook of geometric
topology" (editors R J Daverman, R B Sher),
North-Holland (2002) 93 MR1886669 |
13 |
W W Boone,
The word
problem, Ann. of Math. 70 (1959) 207 MR0179237 |
14 |
M R Bridson,
The geometry of the word problem, from: "Invitations to
geometry and topology" (editors M R Bridson, S M
Salamon), Oxford Grad. Texts Math. 7, Oxford Univ. Press (2002)
29 MR1967746 |
15 |
M R Bridson, A
Haefliger, Metric spaces of
non-positive curvature, 319, Springer (1999) MR1744486 |
16 |
S V Buyalo,
V L Kobel′skiĭ, Geometrization of
graph-manifolds, I :
Conformal geometrization, Algebra i Analiz 7 (1995) 1
MR1347511 |
17 |
S V Buyalo,
V L Kobel′skiĭ, Geometrization of
graph-manifolds, II :
Isometric geometrization, Algebra i Analiz 7 (1995) 96
MR1353491 |
18 |
D Calegari, D
Gabai, Shrinkwrapping
and the taming of hyperbolic 3–manifolds, J. Amer. Math. Soc. 19
(2006) 385 MR2188131 |
19 |
R Charney, An introduction
to right-angled Artin groups, Geom. Dedicata 125 (2007)
141 MR2322545 |
20 |
F Dahmani, D
Groves, The isomorphism
problem for toral relatively hyperbolic groups, Publ.
Math. Inst. Hautes Études Sci. (2008) 211 MR2434694 |
21 |
F Dahmani, V
Guirardel, Foliations for
solving equations in groups: Free, virtually free, and
hyperbolic groups, J. Topol. 3 (2010) 343 MR2651364 |
22 |
F Dahmani, V
Guirardel, The isomorphism
problem for all hyperbolic groups, Geom. Funct. Anal.
21 (2011) 223 MR2795509 |
23 |
M Dehn, Über unendliche
diskontinuierliche Gruppen, Math. Ann. 71 (1911) 116
MR1511645 |
24 |
V H Dyson, The
word problem and residually finite groups, Not. Amer. Math.
Soc. 11 (1964) 734 |
25 |
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 (1992) MR1161694 |
26 |
T Evans, Some connections
between residual finiteness, finite embeddability and the word
problem, J. London Math. Soc. 1 (1969) 399 MR0249344 |
27 |
S Friedl, T
Kitayama, The virtual fibering
theorem for 3–manifolds,
Enseign. Math. 60 (2014) 79 MR3262436 |
28 |
S Friedl, H
Wilton, The membership problem for 3–manifold groups is solvable, preprint
(2014) arXiv:1401.2648 |
29 |
M Gromov, Hyperbolic
groups, from: "Essays in group theory" (editor S M
Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75
MR919829 |
30 |
D Groves, J F
Manning, H Wilton, Recognizing geometric
3–manifold groups using the word
problem, preprint (2012) arXiv:1210.2101 |
31 |
F Haglund, Finite index
subgroups of graph products, Geom. Dedicata 135 (2008)
167 MR2413337 |
32 |
F Haglund, D T
Wise, Special cube
complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497 |
33 |
W Haken, Theorie der
Normalflächen, Acta Math. 105 (1961) 245 MR0141106 |
34 |
W Haken, Über das
Homöomorphieproblem der 3–Mannigfaltigkeiten, I, Math. Z. 80
(1962) 89 MR0160196 |
35 |
E Hamilton, H
Wilton, P A Zalesskii, Separability of double
cosets and conjugacy classes in 3–manifold groups, J. Lond. Math. Soc.
87 (2013) 269 MR3022716 |
36 |
J Hass, J C
Lagarias, N Pippenger, The computational
complexity of knot and link problems, J. ACM 46 (1999)
185 MR1693203 |
37 |
W Heil, On Kneser’s
conjecture for bounded 3–manifolds, Proc. Cambridge Philos.
Soc. 71 (1972) 243 MR0312503 |
38 |
G Hemion, On the classification of
homeomorphisms of 2–manifolds and
the classification of 3–manifolds, Acta Math. 142 (1979) 123
MR512214 |
39 |
J Hempel,
3–manifolds, 86, Princeton
Univ. Press (1976) MR0415619 |
40 |
J Hempel, Residual
finiteness for 3–manifolds,
from: "Combinatorial group theory and topology" (editors
S M Gersten, J R Stallings), Ann. of Math. Stud. 111,
Princeton Univ. Press (1987) 379 MR895623 |
41 |
R Herken, editor,
The
universal Turing machine : A half-century survey, 2,
Springer (1995) MR1362572 |
42 |
J E Hopcroft,
J D Ullman, Introduction to automata theory,
languages, and computation, Addison-Wesley (1979) MR645539 |
43 |
G C Hruska,
Relative
hyperbolicity and relative quasiconvexity for countable
groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983 |
44 |
S V Ivanov,
The
computational complexity of basic decision problems in
3-dimensional topology, Geom. Dedicata 131 (2008) 1
MR2369189 |
45 |
W Jaco, D
Letscher, J H Rubinstein, Algorithms for
essential surfaces in 3–manifolds, from: "Topology and
geometry : commemorating SISTAG" (editors A J
Berrick, M C Leung, X Xu), Contemp. Math. 314, Amer. Math.
Soc. (2002) 107 MR1941626 |
46 |
W Jaco, U
Oertel, An algorithm
to decide if a 3–manifold is a
Haken manifold, Topology 23 (1984) 195 MR744850 |
47 |
W Jaco, J H
Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65
(2003) 61 MR2057531 |
48 |
W H Jaco,
P B Shalen, Seifert fibered spaces in
3–manifolds, 220, Amer.
Math. Soc. (1979) MR539411 |
49 |
W Jaco, J L
Tollefson, Algorithms for
the complete decomposition of a closed 3–manifold, Illinois J. Math. 39 (1995)
358 MR1339832 |
50 |
K Johannson,
Homotopy equivalences of 3–manifolds with boundaries, 761, Springer
(1979) MR551744 |
51 |
I Kapovich, R
Weidmann, A Miasnikov, Foldings, graphs
of groups and the membership problem, Internat. J.
Algebra Comput. 15 (2005) 95 MR2130178 |
52 |
O Kharlampovich, A
Myasnikov, Elementary
theory of free non-abelian groups, J. Algebra 302
(2006) 451 MR2293770 |
53 |
O Kharlampovich, A
Myasnikov, On Tarski’s decidability problem,
preprint (2014) arXiv:1402.0482 |
54 |
O Kharlampovich, A
Myasnikov, Decidability of the elementary theory of a
torsion-free hyperbolic group, preprint (2015) arXiv:1303.0760 |
55 |
H Kneser,
Geschlossene Flächen in dreidimensionalen
Mannigfaltigkeiten, Jahresber. Dtsch. Math.-Ver. 38 (1929)
248 |
56 |
P Koiran, Hilbert’s
Nullstellensatz is in the polynomial hierarchy, J.
Complexity 12 (1996) 273 MR1422712 |
57 |
G Kuperberg,
Knottedness is in
NP, modulo GRH, Adv. Math. 256 (2014) 493 MR3177300 |
58 |
G Kuperberg,
Algorithmic homeomorphism of 3–manifolds as a corollary of
geometrization, preprint (2015) arXiv:1508.06720 |
59 |
B Leeb, 3–manifolds with(out) metrics of nonpositive
curvature, Invent. Math. 122 (1995) 277 MR1358977 |
60 |
H Liang, Equation problem
over central extensions of hyperbolic groups, J. Topol.
Anal. 6 (2014) 167 MR3191648 |
61 |
R C Lyndon,
P E Schupp, Combinatorial group theory, 89,
Springer (1977) MR0577064 |
62 |
G S Makanin,
Equations in a free group, Izv. Akad. Nauk SSSR Ser.
Mat. 46 (1982) 1199 MR682490 |
63 |
J Manning, Algorithmic detection
and description of hyperbolic structures on closed 3–manifolds with solvable word problem,
Geom. Topol. 6 (2002) 1 MR1885587 |
64 |
D Marker, Model
theory, 217, Springer (2002) MR1924282 |
65 |
A Markov, The
insolubility of the problem of homeomorphy, Dokl. Akad.
Nauk SSSR 121 (1958) 218 MR0097793 |
66 |
S Matveev, Algorithmic
topology and classification of 3–manifolds, 9, Springer (2003)
MR1997069 |
67 |
J C C
McKinsey, The decision problem for
some classes of sentences without quantifiers, J.
Symbolic Logic 8 (1943) 61 MR0008991 |
68 |
K A Mihaĭlova,
The occurrence problem for direct products of groups,
Dokl. Akad. Nauk SSSR 119 (1958) 1103 MR0100018 |
69 |
K A Mihaĭlova,
The occurrence problem for free products of groups,
Dokl. Akad. Nauk SSSR 127 (1959) 746 MR0106940 |
70 |
K A Mihaĭlova,
The occurrence problem for direct products of groups,
Mat. Sb. 70 (112) (1966) 241 MR0194497 |
71 |
K A Mihaĭlova,
The occurrence problem for free products of groups, Mat.
Sb. 75 (117) (1968) 199 MR0222179 |
72 |
C F Miller III,
Decision
problems for groups — Survey and reflections, from:
"Algorithms and classification in combinatorial group theory"
(editor G Baumslag), Math. Sci. Res. Inst. Publ. 23, Springer
(1992) 1 MR1230627 |
73 |
J Milnor, A unique decomposition
theorem for 3–manifolds,
Amer. J. Math. 84 (1962) 1 MR0142125 |
74 |
A Minasyan,
Hereditary
conjugacy separability of right-angled Artin groups and its
applications, Groups Geom. Dyn. 6 (2012) 335 MR2914863 |
75 |
E E Moise,
Affine
structures in 3–manifolds,
V : The triangulation
theorem and Hauptvermutung, Ann. of Math. 56 (1952) 96
MR0048805 |
76 |
E E Moise,
Geometric topology in dimensions 2 and 3, 47,
Springer (1977) MR0488059 |
77 |
J Morgan, G
Tian, Ricci flow and the Poincaré conjecture, 3,
Amer. Math. Soc. (2007) MR2334563 |
78 |
J Morgan, G
Tian, The geometrization conjecture, 5, Amer. Math.
Soc. (2014) MR3186136 |
79 |
A W Mostowski,
On the decidability of some problems in special classes of
groups, Fund. Math. 59 (1966) 123 MR0224693 |
80 |
G A Niblo,
Separability
properties of free groups and surface groups, J. Pure
Appl. Algebra 78 (1992) 77 MR1154898 |
81 |
G A Niblo,
D T Wise, Subgroup
separability, knot groups and graph manifolds, Proc.
Amer. Math. Soc. 129 (2001) 685 MR1707529 |
82 |
P S Novikov,
Unsolvability of the conjugacy problem in the theory of
groups, Izv. Akad. Nauk SSSR. Ser. Mat. 18 (1954) 485
MR0075196 |
83 |
P S Novikov,
On the algorithmic insolvability of the word problem in
group theory, 9, Amer. Math. Soc. (1958) 1 MR0075197 |
84 |
P Papasoglu,
On the
sub-quadratic isoperimetric inequality, from:
"Geometric group theory" (editors R Charney, M Davis, M
Shapiro), Ohio State Univ. MSRI Publ. 3, de Gruyter (1995) 149
MR1355100 |
85 |
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 |
86 |
G Perelman, The
entropy formula for the Ricci flow and its geometric
applications, preprint (2002) arXiv:math/0211159 |
87 |
G Perelman, Finite
extinction time for the solutions to the Ricci flow on certain
three-manifolds, preprint (2003) arXiv:math/0307245 |
88 |
G Perelman, Ricci
flow with surgery on three-manifolds, preprint (2003)
arXiv:math/0303109 |
89 |
B Poonen,
Undecidable problems: A sampler, from: "Interpreting
Gödel : Critical essays" (editor J Kennedy), Cambridge
Univ. Press (2014) 211 |
90 |
J P Préaux,
Conjugacy problem
in groups of oriented geometrizable 3–manifolds, Topology 45 (2006) 171
MR2170497 |
91 |
J P Préaux,
The conjugacy problem in groups of non-orientable
3–manifolds, preprint (2013)
arXiv:1202.4148 |
92 |
P Przytycki,
D T Wise, Separability of
embedded surfaces in 3–manifolds, Compos. Math. 150 (2014)
1623 MR3260144 |
93 |
M O Rabin,
Recursive
unsolvability of group theoretic problems, Ann. of
Math. 67 (1958) 172 MR0110743 |
94 |
K Reidemeister,
Homotopieringe und
Linsenräume, Abh. Math. Sem. Univ. Hamburg 11 (1935)
102 MR3069647 |
95 |
E Rips, Z Sela,
Canonical
representatives and equations in hyperbolic groups,
Invent. Math. 120 (1995) 489 MR1334482 |
96 |
J H Rubinstein,
An algorithm to recognize the 3–sphere, from: "Proc. ICM, Vol. 1, 2"
(editor S D Chatterji), Birkhäuser (1995) 601 MR1403961 |
97 |
S Schleimer,
Sphere
recognition lies in NP, from: "Low-dimensional and
symplectic topology" (editor M Usher), Proc. Sympos. Pure Math.
82, Amer. Math. Soc. (2011) 183 MR2768660 |
98 |
P Scott, Subgroups of
surface groups are almost geometric, J. London Math.
Soc. 17 (1978) 555 MR0494062 |
99 |
P Scott, The geometries of
3–manifolds, Bull. London
Math. Soc. 15 (1983) 401 MR705527 |
100 |
P Scott, There are no fake Seifert
fibre spaces with infinite π1, Ann. of Math. 117 (1983) 35
MR683801 |
101 |
P Scott, H
Short, The homeomorphism
problem for closed 3–manifolds, Algebr. Geom. Topol. 14
(2014) 2431 MR3331689 |
102 |
Z Sela, The conjugacy
problem for knot groups, Topology 32 (1993) 363
MR1217075 |
103 |
Z Sela, The isomorphism problem for
hyperbolic groups, I, Ann. of Math. 141 (1995) 217
MR1324134 |
104 |
Z Sela, A report on
Tarski’s decidability problem, preprint (2014) arXiv:1401.5711 |
105 |
J P Serre,
Trees, Springer (1980) MR607504 |
106 |
C C Sims,
Computation with
finitely presented groups, 48, Cambridge Univ. Press
(1994) MR1267733 |
107 |
J Stallings,
Grushko’s theorem, II : Kneser’s conjecture, Not.
Amer. Math. Soc. 6 (1959) 531 |
108 |
J Stillwell,
The word
problem and the isomorphism problem for groups, Bull.
Amer. Math. Soc. 6 (1982) 33 MR634433 |
109 |
A Thompson,
Thin
position and the recognition problem for S3, Math. Res. Lett. 1 (1994) 613
MR1295555 |
110 |
W P Thurston,
Three-dimensional
manifolds, Kleinian groups and hyperbolic geometry,
Bull. Amer. Math. Soc. 6 (1982) 357 MR648524 |
111 |
A M Turing,
On
computable numbers, with an application to the
Entscheidungsproblem, Proc. London Math. Soc. S2-42230
MR1577030 |
112 |
F Waldhausen,
On irreducible
3–manifolds which are sufficiently
large, Ann. of Math. 87 (1968) 56 MR0224099 |
113 |
F Waldhausen,
Recent results on sufficiently large 3–manifolds, from: "Algebraic and geometric
topology, Part 2" (editor R J Milgram), Proc. Sympos. Pure
Math. 32, Amer. Math. Soc. (1978) 21 MR520520 |
114 |
D T Wise,
Research
announcement: The structure of groups with a quasiconvex
hierarchy, Electron. Res. Announc. Math. Sci. 16 (2009)
44 MR2558631 |
115 |
D T Wise, From
riches to raags :
3–manifolds, right-angled Artin
groups, and cubical geometry, 117, Amer. Math. Soc.
(2012) |
116 |
D T Wise,
The structure of
groups with a quasi-convex hierarchy (2012) |