Volume 11, issue 5 (2011)

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

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The cactus tree of a metric space

Panos Papasoglu and Eric Swenson

Algebraic & Geometric Topology 11 (2011) 2547–2578
Bibliography
1 J M Aarts, T Nishiura, Dimension and extensions, North-Holland Math. Library 48, North-Holland (1993) MR1206002
2 S A Adeleke, P M Neumann, Relations related to betweenness: their structure and automorphisms, Mem. Amer. Math. Soc. 131, no. 623, Amer. Math. Soc. (1998) MR1388893
3 M Bestvina, G Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991) 469 MR1096169
4 B H Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998) 145 MR1638764
5 B H Bowditch, Group actions on trees and dendrons, Topology 37 (1998) 1275 MR1632928
6 B H Bowditch, Treelike structures arising from continua and convergence groups, Mem. Amer. Math. Soc. 139, no. 662, Amer. Math. Soc. (1999) MR1483830
7 I M Chiswell, Generalised trees and $\Lambda$–trees, from: "Combinatorial and geometric group theory (Edinburgh, 1993)" (editors A J Duncan, N D Gilbert, J Howie), London Math. Soc. Lecture Note Ser. 204, Cambridge Univ. Press (1995) 43 MR1320273
8 E A Dinic, A V Karzanov, M V Lomonosov, The structure of a system of minimal edge cuts of a graph, from: "Studies in discrete optimization" (editor A A Fridman), Izdat. “Nauka” (1976) 290 MR0498241
9 T Fleiner, A Frank, A quick proof for the cactus representation theorem of mincuts, preprint (2009)
10 H Freudenthal, Neuaufbau der Endentheorie, Ann. of Math. $(2)$ 43 (1942) 261 MR0006504
11 D P Guralnik, Ends of cusp-uniform groups of locally connected continua. I, Internat. J. Algebra Comput. 15 (2005) 765 MR2160578
12 F Kammer, H Täubig, Connectivity, from: "Network Analysis" (editors U Brandes, T Erlebach), Lecture Notes in Comp. Sci. 3418, Springer (2005) 143
13 K Kuratowski, Topology. Vol. I, Academic Press (1966) MR0217751
14 G Levitt, Non-nesting actions on real trees, Bull. London Math. Soc. 30 (1998) 46 MR1479035
15 K Morita, On bicompactifications of semibicompact spaces, Sci. Rep. Tokyo Bunrika Daigaku. Sect. A. 4 (1952) 222 MR0052089
16 D Naor, V V Vazirani, Representing and enumerating edge connectivity cuts in $\mathcal {RNC}$, from: "Algorithms and data structures, Proc. 2nd Workshop, WADS '91, (Ottawa, Canada, 1991)" (editors F Dehne, J R Sack, N Santoro), Lecture Notes in Comp. Sci 519, Springer (1991) 273
17 P Papasoglu, E Swenson, Convergence groups and cactus trees, in preparation
18 P Papasoglu, E Swenson, From continua to $\mathbb R$–trees, Algebr. Geom. Topol. 6 (2006) 1759 MR2263049
19 P Papasoglu, E Swenson, Boundaries and JSJ decompositions of $\mathrm{CAT}(0)$–groups, Geom. Funct. Anal. 19 (2009) 559 MR2545250
20 G A Swarup, On the cut point conjecture, Electron. Res. Announc. Amer. Math. Soc. 2 (1996) 98 MR1412948
21 E Swenson, A cut point theorem for $\mathrm{CAT}(0)$ groups, J. Differential Geom. 53 (1999) 327 MR1802725
22 E Swenson, A cutpoint tree for a continuum, from: "Computational and geometric aspects of modern algebra (Edinburgh, 1998)" (editors M Atkinson, N Gilbert, J Howie, S Linton, E Robertson), London Math. Soc. Lecture Note Ser. 275, Cambridge Univ. Press (2000) 254 MR1776779
23 W T Tutte, Connectivity in graphs, Math. Expositions 15, Univ. of Toronto Press (1966) MR0210617
24 W T Tutte, Graph theory, Encyclopedia of Math. and its Appl. 21, Addison-Wesley (1984) MR746795
25 L E Ward Jr., Axioms for cutpoints, from: "General topology and modern analysis (Proc. Conf., Univ. California, Riverside, 1980)" (editors L F McAuley, M M Rao), Academic Press (1981) 327 MR619058
26 G T Whyburn, Concerning the structure of a continuous curve, Amer. J. Math. 50 (1928) 167 MR1506664