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Connectedness properties and splittings of groups with isolated flats

G Christopher Hruska and Kim Ruane

Algebraic & Geometric Topology 21 (2021) 755–800
Bibliography
1 F D Ancel, L Siebenmann, The construction of homogeneous homology manifolds, Abstracts Amer. Math. Soc. 6 (1985)
2 W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995) MR1377265
3 M Ben-Zvi, Boundaries of groups with isolated flats are path connected, preprint (2019) arXiv:1909.12360
4 N Benakli, Polyèdres hyperboliques : passage du local au global, PhD thesis, Université Paris-Sud (1992)
5 M Bestvina, Local homology properties of boundaries of groups, Michigan Math. J. 43 (1996) 123 MR1381603
6 M Bestvina, G Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991) 469 MR1096169
7 N Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann (1971) MR0358652
8 M Bourdon, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geom. Funct. Anal. 7 (1997) 245 MR1445387
9 B H Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998) 145 MR1638764
10 B H Bowditch, Treelike structures arising from continua and convergence groups, 662, Amer. Math. Soc. (1999) MR1483830
11 B H Bowditch, Peripheral splittings of groups, Trans. Amer. Math. Soc. 353 (2001) 4057 MR1837220
12 B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) MR2922380
13 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
14 C E Capel, Inverse limit spaces, Duke Math. J. 21 (1954) 233 MR62417
15 C Champetier, Propriétés statistiques des groupes de présentation finie, Adv. Math. 116 (1995) 197 MR1363765
16 C B Croke, B Kleiner, Spaces with nonpositive curvature and their ideal boundaries, Topology 39 (2000) 549 MR1746908
17 F Dahmani, V Guirardel, P Przytycki, Random groups do not split, Math. Ann. 349 (2011) 657 MR2755002
18 P Dani, M Haulmark, G Walsh, Right-angled Coxeter groups with non-planar boundary, preprint (2019) arXiv:1902.01029
19 R J Daverman, Decompositions of manifolds, 124, Academic (1986) MR872468
20 R Geoghegan, E Swenson, On semistability of CAT(0) groups, Groups Geom. Dyn. 13 (2019) 695 MR3950647
21 C R Guilbault, Weak 𝒵–structures for some classes of groups, Algebr. Geom. Topol. 14 (2014) 1123 MR3180829
22 M Haulmark, Boundary classification and two-ended splittings of groups with isolated flats, J. Topol. 11 (2018) 645 MR3830879
23 M Haulmark, G C Hruska, B Sathaye, Nonhyperbolic Coxeter groups with Menger boundary, Enseign. Math. 65 (2019) 207 MR4057359
24 J G Hocking, G S Young, Topology, Addison-Wesley (1961) MR0125557
25 G C Hruska, Nonpositively curved 2–complexes with isolated flats, Geom. Topol. 8 (2004) 205 MR2033482
26 G C Hruska, B Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005) 1501 MR2175151
27 G C Hruska, B Kleiner, Erratum to “Hadamard spaces with isolated flats”, Geom. Topol. 13 (2009) 699 MR2469527
28 G C Hruska, K Ruane, Hierarchies and semistability of relatively hyperbolic groups, preprint (2019) arXiv:1904.12947
29 W Jakobsche, The Bing–Borsuk conjecture is stronger than the Poincaré conjecture, Fund. Math. 106 (1980) 127 MR580590
30 W Jakobsche, Homogeneous cohomology manifolds which are inverse limits, Fund. Math. 137 (1991) 81 MR1113561
31 M Kapovich, B Kleiner, Hyperbolic groups with low-dimensional boundary, Ann. Sci. École Norm. Sup. 33 (2000) 647 MR1834498
32 M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of 3–manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
33 J Krasinkiewicz, Local connectedness and pointed 1–movability, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977) 1265 MR500986
34 G Levitt, Non-nesting actions on real trees, Bull. London Math. Soc. 30 (1998) 46 MR1479035
35 L Louder, N Touikan, Strong accessibility for finitely presented groups, Geom. Topol. 21 (2017) 1805 MR3650082
36 M Mihalik, K Ruane, CAT(0) groups with non-locally connected boundary, J. London Math. Soc. 60 (1999) 757 MR1753812
37 M Mihalik, K Ruane, CAT(0) HNN–extensions with non-locally connected boundary, Topology Appl. 110 (2001) 83 MR1804700
38 M Mihalik, E Swenson, Relatively hyperbolic groups with semistable fundamental group at infinity, J. Topol. 14 (2021) 39 MR4186133
39 M A Moran, Metrics on visual boundaries of CAT(0) spaces, Geom. Dedicata 183 (2016) 123 MR3523122
40 P Ontaneda, Cocompact CAT(0) spaces are almost geodesically complete, Topology 44 (2005) 47 MR2104000
41 D Osajda, J Świątkowski, On asymptotically hereditarily aspherical groups, Proc. Lond. Math. Soc. 111 (2015) 93 MR3404777
42 L S Pontryagin, Sur une hypothèse fundamentale de la théorie de la dimension, C.R. Acad. Sci. Paris 190 (1930) 1105
43 K Ruane, CAT(0) boundaries of truncated hyperbolic space, Topology Proc. 29 (2005) 317 MR2182938
44 J P Serre, Arbres, amalgames, SL2, 46, Soc. Math. France (1977) MR0476875
45 G A Swarup, On the cut point conjecture, Electron. Res. Announc. Amer. Math. Soc. 2 (1996) 98 MR1412948
46 J Świątkowski, Trees of metric compacta and trees of manifolds, Geom. Topol. 24 (2020) 533 MR4153649
47 H C Tran, Relations between various boundaries of relatively hyperbolic groups, Internat. J. Algebra Comput. 23 (2013) 1551 MR3143594
48 A Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004) 41 MR2039323