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The simplicial boundary of a CAT(0) cube complex

Mark F Hagen

Algebraic & Geometric Topology 13 (2013) 1299–1367
Bibliography
1 W Ballmann, M Gromov, V Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics 61, Birkhäuser (1985) MR823981
2 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
3 J Behrstock, R Charney, Divergence and quasimorphisms of right-angled Artin groups, Math. Ann. 352 (2012) 339 MR2874959
4 M R Bridson, Geodesics and curvature in metric simplicial complexes, from: "Group theory from a geometrical viewpoint" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. Publ., River Edge, NJ (1991) 373 MR1170372
5 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer (1999) MR1744486
6 P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012
7 R Charney, M W Davis, Finite $K(\pi, 1)$s for Artin groups, from: "Prospects in topology" (editor F Quinn), Ann. of Math. Stud. 138, Princeton Univ. Press (1995) 110 MR1368655
8 R Charney, M W Davis, The $K(\pi,1)$–problem for hyperplane complements associated to infinite reflection groups, J. Amer. Math. Soc. 8 (1995) 597 MR1303028
9 I Chatterji, G Niblo, From wall spaces to ${\\mathrm CAT}(0)$ cube complexes, Internat. J. Algebra Comput. 15 (2005) 875 MR2197811
10 V Chepoi, Graphs of some $\mathrm{CAT}(0)$ complexes, Adv. in Appl. Math. 24 (2000) 125 MR1748966
11 V Chepoi, Nice labeling problem for event structures: a counterexample, SIAM J. Comput. 41 (2012) 715 MR2974750
12 V Chepoi, M Hagen, On embeddings of $\mathrm{CAT}(0)$ cube complexes into products of trees arXiv:1107.0863v1
13 C B Croke, B Kleiner, Spaces with nonpositive curvature and their ideal boundaries, Topology 39 (2000) 549 MR1746908
14 F Dahmani, V Guirardel, P Przytycki, Random groups do not split, Math. Ann. 349 (2011) 657 MR2755002
15 D Epstein, J C Falmagne, S Ovchinnikov, Media theory, Springer (2008) MR2368792
16 D S Farley, Finiteness and $\mathrm{CAT}(0)$ properties of diagram groups, Topology 42 (2003) 1065 MR1978047
17 D S Farley, Actions of picture groups on CAT(0) cubical complexes, Geom. Dedicata 110 (2005) 221 MR2136028
18 S M Gersten, Divergence in $3$–manifold groups, Geom. Funct. Anal. 4 (1994) 633 MR1302334
19 S M Gersten, Quadratic divergence of geodesics in $\mathrm{CAT}(0)$ spaces, Geom. Funct. Anal. 4 (1994) 37 MR1254309
20 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
21 M Hagen, Weak hyperbolicity of cube complexes and quasi-arboreal groups arXiv:1101.5191v5
22 M Hagen, Geometry and combinatorics of cube complexes, Ph.D. thesis, McGill University (2012)
23 F Haglund, Isometries of CAT(0) cube complexes are semi-simple arXiv:0705.3386
24 F Haglund, F Paulin, Simplicité de groupes d'automorphismes d'espaces à courbure négative, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1 (1998) 181 MR1668359
25 C H Houghton, Ends of locally compact groups and their coset spaces, J. Austral. Math. Soc. 17 (1974) 274 MR0357679
26 C Hruska, D T Wise, Finiteness properties of cubulated groups, Preprint (2010)
27 W Imrich, S Klavžar, Product graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience (2000) MR1788124
28 J R Isbell, Median algebra, Trans. Amer. Math. Soc. 260 (1980) 319 MR574784
29 M Kapovich, B Leeb, $3$–manifold groups and nonpositive curvature, Geom. Funct. Anal. 8 (1998) 841 MR1650098
30 I Leary, A metric Kan–Thurston theorem, Preprint (2010)
31 A Nevo, M Sageev, The Poisson boundary of CAT(0) cube complex groups arXiv:1105.1675v1
32 G A Niblo, L D Reeves, Coxeter groups act on $\mathrm{CAT}(0)$ cube complexes, J. Group Theory 6 (2003) 399 MR1983376
33 B Nica, Cubulating spaces with walls, Algebr. Geom. Topol. 4 (2004) 297 MR2059193
34 Y Ollivier, D T Wise, Cubulating random groups at density less than $1/6$, Trans. Amer. Math. Soc. 363 (2011) 4701 MR2806688
35 M A Roller, Poc Sets, Median Algebras and Group Actions (1998)
36 M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
37 P Scott, Ends of pairs of groups, J. Pure Appl. Algebra 11 (1977) 179 MR487104
38 M L J van de Vel, Theory of convex structures, North-Holland Mathematical Library 50, North-Holland Publishing Co. (1993) MR1234493
39 D T Wise, Cubulating small cancellation groups, Geom. Funct. Anal. 14 (2004) 150 MR2053602
40 D T Wise, The structure of groups with a quasiconvex hierarchy, Preprint (2011)