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Helly groups
Jérémie Chalopin, Victor Chepoi, Anthony Genevois,
Hiroshi Hirai and Damian Osajda
Geometry & Topology 29 (2025) 1–70
1
J A Altobelli ,
The
word problem for Artin groups of FC type , J. Pure Appl.
Algebra 129 (1998) 1 MR1626651
2
N Aronszajn , P
Panitchpakdi , Extension of uniformly
continuous transformations and hyperconvex metric
spaces , Pacific J. Math. 6 (1956) 405 MR0084762
3
H J Bandelt ,
Hereditary
modular graphs , Combinatorica 8 (1988) 149 MR0963122
4
H J Bandelt , V
Chepoi , Metric graph theory
and geometry: a survey , from: "Surveys on discrete and
computational geometry" (editors J E Goodman, J Pach, R
Pollack), Contemp. Math. 453, Amer. Math. Soc. (2008) 49
MR2405677
5
H J Bandelt , V
Chepoi , D Eppstein , Combinatorics and geometry
of finite and infinite squaregraphs , SIAM J. Discrete
Math. 24 (2010) 1399 MR2735930
6
H J Bandelt ,
H M Mulder , Pseudomodular
graphs , Discrete Math. 62 (1986) 245 MR0866940
7
H J Bandelt ,
H M Mulder , E Wilkeit , Quasi-median graphs
and algebras , J. Graph Theory 18 (1994) 681 MR1297190
8
H J Bandelt , E
Pesch , Dismantling
absolute retracts of reflexive graphs , European J.
Combin. 10 (1989) 211 MR1029165
9
H J Bandelt , E
Prisner , Clique graphs
and Helly graphs , J. Combin. Theory Ser. B 51 (1991) 34
MR1088625
10
H J Bandelt , M
van de Vel , Superextensions
and the depth of median graphs , J. Combin. Theory Ser.
A 57 (1991) 187 MR1111556
11
J A Barmak ,
E G Minian , Strong homotopy
types, nerves and collapses , Discrete Comput. Geom. 47
(2012) 301 MR2872540
12
A Bartels , W
Lück , The Borel
conjecture for hyperbolic and CAT (0) -groups , Ann. of Math. 175 (2012)
631 MR2993750
13
C Berge ,
Hypergraphs: combinatorics of finite sets , 45,
North-Holland (1989) MR1013569
14
C Berge , P
Duchet , A generalization of Gilmore’s theorem , from:
"Recent advances in graph theory" (editor M Fiedler), Academia
(1975) 49 MR0406801
15
C Berge , M Las
Vergnas , Sur un
théorème du type König pour hypergraphes , Ann. New York
Acad. Sci. 175 (1970) 32 MR0266787
16
M Bestvina ,
Local
homology properties of boundaries of groups , Michigan
Math. J. 43 (1996) 123 MR1381603
17
A Björner ,
Topological methods , from: "Handbook of combinatorics,
II" (editors R L Graham, M Grötschel, L Lovász), Elsevier
(1995) 1819 MR1373690
18
K Borsuk , On the imbedding of
systems of compacta in simplicial complexes , Fund.
Math. 35 (1948) 217 MR0028019
19
B H Bowditch ,
Median
and injective metric spaces , Math. Proc. Cambridge
Philos. Soc. 168 (2020) 43 MR4043820
20
T Brady , J P
McCammond , Three-generator
Artin groups of large type are biautomatic , J. Pure
Appl. Algebra 151 (2000) 1 MR1770639
21
M R Bridson , A
Haefliger , Metric spaces of
non-positive curvature , 319, Springer (1999) MR1744486
22
P J Cameron ,
Dual polar
spaces , Geom. Dedicata 12 (1982) 75 MR0645040
23
J Chalopin , V
Chepoi , H Hirai , D Osajda , Weakly modular graphs and
nonpositive curvature , 1309, Amer. Math. Soc. (2020)
MR4223822
24
R Charney , Artin groups of finite
type are biautomatic , Math. Ann. 292 (1992) 671
MR1157320
25
V D Chepoi ,
Classification of graphs by means of metric triangles ,
Metody Diskret. Analiz. (1989) 75 MR1114014
26
V Chepoi , A note on
r -dominating cliques ,
Discrete Math. 183 (1998) 47 MR1606788
27
V Chepoi , Graphs of some
CAT (0)
complexes , Adv. in Appl. Math. 24 (2000) 125 MR1748966
28
V Chepoi , F F
Dragan , B Estellon , M Habib , Y Vaxès ,
Diameters,
centers, and approximating trees of δ -hyperbolic geodesic spaces and
graphs , from: "Symposium on computational geometry",
ACM (2008) 59 MR2504271
29
V Chepoi , B
Estellon , Packing and
covering δ -hyperbolic spaces by
balls , from: "Approximation, randomization, and
combinatorial optimization: algorithms and techniques" (editors
M Charikar, K Jansen, O Reingold, J D P Rolim),
Lecture Notes in Comput. Sci. 4627, Springer (2007) 59
30
V Chepoi , K
Knauer , T Marc , Hypercellular
graphs : partial cubes without Q 3 −
as partial cube minor , Discrete Math. 343 (2020) 111678
MR4065838
31
M Chrobak , L L
Larmore , Generosity helps or an
11 -competitive algorithm for three
servers , J. Algorithms 16 (1994) 234 MR1258238
32
D Descombes ,
Asymptotic rank of
spaces with bicombings , Math. Z. 284 (2016) 947
MR3563261
33
D Descombes , U
Lang , Convex geodesic
bicombings and hyperbolicity , Geom. Dedicata 177 (2015)
367 MR3370039
34
D Descombes , U
Lang , Flats in spaces with
convex geodesic bicombings , Anal. Geom. Metr. Spaces 4
(2016) 68 MR3483604
35
F F Dragan ,
Центры в графах и своıство
Хелли , PhD thesis, Moldova
State University (1989)
36
F F Dragan ,
H M Guarnera , Obstructions to a
small hyperbolicity in Helly graphs , Discrete Math. 342
(2019) 326 MR3873004
37
A W M Dress ,
Trees, tight
extensions of metric spaces, and the cohomological dimension of
certain groups: a note on combinatorial properties of metric
spaces , Adv. Math. 53 (1984) 321 MR0753872
38
A W M Dress ,
A note on compact
groups, acting on ℝ -trees ,
Beitr. Algebra Geom. 29 (1989) 81 MR1036092
39
A W M Dress ,
R Scharlau , Gated sets in metric
spaces , Aequationes Math. 34 (1987) 112 MR915878
40
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 & Bartlett (1992) MR1161694
41
F Escalante ,
Über iterierte
Clique-Graphen , Abh. Math. Sem. Univ. Hamburg 39 (1973)
59 MR0329947
42
M Farber , R E
Jamison , On local
convexity in graphs , Discrete Math. 66 (1987) 231
MR0900046
43
F T Farrell ,
J F Lafont , EZ-structures and topological
applications , Comment. Math. Helv. 80 (2005) 103
MR2130569
44
T Fukaya , S i
Oguni , A coarse
Cartan–Hadamard theorem with application to the coarse
Baum–Connes conjecture , J. Topol. Anal. 12 (2020) 857
MR4139217
45
A Genevois ,
Cubical-like geometry of quasi-median graphs and
applications to geometric group theory , PhD thesis,
Aix-Marseille Université (2017) arXiv:1712.01618
46
R Geoghegan ,
Topological methods
in group theory , 243, Springer (2008) MR2365352
47
S M Gersten ,
H B Short , Small cancellation theory
and automatic groups , Invent. Math. 102 (1990) 305
MR1074477
48
O Goodman , V
Moulton , On the tight
span of an antipodal graph , Discrete Math. 218 (2000)
73 MR1754328
49
M Gromov , Hyperbolic
groups , from: "Essays in group theory" (editor S M
Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75
MR0919829
50
V S Guba ,
M V Sapir , On subgroups of the R Thompson
group F and other diagram
groups , Mat. Sb. 190 (1999) 3 MR1725439
51
A Hatcher , Algebraic
topology , Cambridge Univ. Press (2002) MR1867354
52
P Hell , I
Rival , Absolute retracts and
varieties of reflexive graphs , Canad. J. Math. 39
(1987) 544 MR0905743
53
S Hensel , D
Osajda , P Przytycki , Realisation and
dismantlability , Geom. Topol. 18 (2014) 2079 MR3268774
54
N Hoda , Quadric
complexes , Michigan Math. J. 69 (2020) 241 MR4104372
55
N Hoda , Crystallographic Helly
groups , Bull. Lond. Math. Soc. 55 (2023) 2991
56
J Huang , D
Osajda , Large-type Artin groups
are systolic , Proc. Lond. Math. Soc. 120 (2020) 95
MR3999678
57
J Huang , D
Osajda , Helly meets
Garside and Artin , Invent. Math. 225 (2021) 395
MR4285138
58
S Hughes , M
Valiunas , Commensurating HNN-extensions: hierarchical
hyperbolicity and biautomaticity , (2022) arXiv:2203.11996
59
J R Isbell ,
Six theorems
about injective metric spaces , Comment. Math. Helv. 39
(1964) 65 MR0182949
60
J R Isbell ,
Median
algebra , Trans. Amer. Math. Soc. 260 (1980) 319
MR0574784
61
T Januszkiewicz , J
Świątkowski , Simplicial
nonpositive curvature , Publ. Math. Inst. Hautes Études
Sci. 104 (2006) 1 MR2264834
62
E M Jawhari , M
Pouzet , D Misane , Retracts: graphs and
ordered sets from the metric point of view , from:
"Combinatorics and ordered sets" (editor I Rival), Contemp.
Math. 57, Amer. Math. Soc. (1986) 175 MR0856237
63
M Kapovich , B
Leeb , On
asymptotic cones and quasi-isometry classes of fundamental
groups of 3 -manifolds ,
Geom. Funct. Anal. 5 (1995) 582 MR1339818
64
D Kasprowski , H
Rüping , The Farrell–Jones
conjecture for hyperbolic and CAT (0) -groups
revisited , J. Topol. Anal. 9 (2017) 551 MR3684616
65
U Lang , Injective hulls of
certain discrete metric spaces and groups , J. Topol.
Anal. 5 (2013) 297 MR3096307
66
L Lovász ,
Combinatorial problems and exercises , North-Holland
(1979) 551 MR0537284
67
R C Lyndon ,
P E Schupp , Combinatorial group
theory , 89, Springer (1977) MR577064
68
B Miesch , Gluing hyperconvex
metric spaces , Anal. Geom. Metr. Spaces 3 (2015) 102
MR3349339
69
G A Niblo ,
L D Reeves , The geometry of
cube complexes and the complexity of their fundamental
groups , Topology 37 (1998) 621 MR1604899
70
D Osajda , Residually finite
non-exact groups , Geom. Funct. Anal. 28 (2018) 509
MR3788209
71
D Osajda , Small
cancellation labellings of some infinite graphs and
applications , Acta Math. 225 (2020) 159 MR4176066
72
D Osajda , T
Prytuła , Classifying spaces for
families of subgroups for systolic groups , Groups Geom.
Dyn. 12 (2018) 1005 MR3845715
73
D Osajda , P
Przytycki , Boundaries of
systolic groups , Geom. Topol. 13 (2009) 2807 MR2546621
74
D Peifer , Artin groups of
extra-large type are biautomatic , J. Pure Appl. Algebra
110 (1996) 15 MR1390670
75
E Pesch , Minimal extensions of
graphs to absolute retracts , J. Graph Theory 11 (1987)
585 MR0917206
76
E Pesch , Retracts
of graphs , 110, Athenäum (1988) MR0930269
77
N Polat , Finite invariant simplices
in infinite graphs , Period. Math. Hungar. 27 (1993) 125
MR1291160
78
N Polat , Convexity and
fixed-point properties in Helly graphs , Discrete Math.
229 (2001) 197 MR1815607
79
S J Pride ,
On Tits’
conjecture and other questions concerning Artin and generalized
Artin groups , Invent. Math. 86 (1986) 347 MR0856848
80
A Quilliot ,
On
the Helly property working as a compactness criterion on
graphs , J. Combin. Theory Ser. A 40 (1985) 186 MR0804883
81
M Roller , Poc sets,
median algebras and group actions , Habilitationsschrift,
Universität Regensburg (1998) arXiv:1607.07747
82
M Sageev , Ends of group pairs
and non-positively curved cube complexes , Proc. Lond.
Math. Soc. 71 (1995) 585 MR1347406
83
J P Serre ,
Trees ,
Springer (1980) MR607504
84
V P Soltan ,
V D Chepoi , Conditions for invariance of set
diameters under d -convexification
in a graph , Kibernetika (Kiev) (1983) 14 MR765117
85
J Świątkowski ,
Regular
path systems and (bi)automatic groups , Geom. Dedicata
118 (2006) 23 MR2239447
86
J L Szwarcfiter ,
Recognizing clique-Helly graphs , Ars Combin. 45 (1997)
29 MR1447758
87
M van de Vel ,
Collapsible
polyhedra and median spaces , Proc. Amer. Math. Soc. 126
(1998) 2811 MR1452832
88
D T Wise ,
Cubulating small
cancellation groups , Geom. Funct. Anal. 14 (2004) 150
MR2053602