Volume 21, issue 2 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
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