Algebraic & Geometric Topology Volume 6, issue 5 (2006)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

The $\mathrm{FA}_n$ Conjecture for Coxeter groups

Angela Kubena Barnhill

Algebraic & Geometric Topology 6 (2006) 2117–2150

DOI: 10.2140/agt.2006.6.2117

Bibliography

1	R C Alperin, Platonic triangles of groups, Experiment. Math. 7 (1998) 191 MR1676687
2	H Bass, Groups of integral representation type, Pacific J. Math. 86 (1980) 15 MR586867
3	O V Bogopol’skiĭ, Arborial decomposability of groups of automorphisms of free groups, Algebra i Logika 26 (1987) 131, 271 MR964922
4	N Bourbaki, Lie groups and Lie algebras. Chapters 4–6, Elements of Mathematics (Berlin), Springer (2002) MR1890629
5	N Brady, J Crisp, Two-dimensional Artin groups with $\mathrm{CAT}(0)$ dimension three, from: "Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000)", Geom. Dedicata 94 (2002) 185 MR1950878
6	M R Bridson, Helly's theorem and actions of the automorphism group of a free group
7	M R Bridson, Geodesics and curvature in metric simplicial complexes, from: "Group theory from a geometrical viewpoint (Trieste, 1990)", World Sci. Publ., River Edge, NJ (1991) 373 MR1170372
8	M R Bridson, On the semisimplicity of polyhedral isometries, Proc. Amer. Math. Soc. 127 (1999) 2143 MR1646316
9	M R Bridson, Length functions, curvature and the dimension of discrete groups, Math. Res. Lett. 8 (2001) 557 MR1851271
10	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren series 319, Springer (1999) MR1744486
11	K S Brown, Buildings, Springer (1989) MR969123
12	K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1994) MR1324339
13	D Cooper, D D Long, A W and Reid, Infinite Coxeter groups are virtually indicable, Proc. Edinburgh Math. Soc. $(2)$ 41 (1998) 303 MR1626421
14	J M Corson, Complexes of groups, Proc. London Math. Soc. $(3)$ 65 (1992) 199 MR1162493
15	M Culler, K Vogtmann, A group-theoretic criterion for property $\mathrm{FA}$, Proc. Amer. Math. Soc. 124 (1996) 677 MR1307506
16	M W Davis, The Geometry and Topology of Coxeter Groups
17	M W Davis, G Moussong, Notes on nonpositively curved polyhedra, from: "Low dimensional topology (Eger, 1996/Budapest, 1998)", Bolyai Soc. Math. Stud. 8, János Bolyai Math. Soc. (1999) 11 MR1747268
18	V V Deodhar, On the root system of a Coxeter group, Comm. Algebra 10 (1982) 611 MR647210
19	B Farb, Group actions and Helly's theorem
20	C Gonciulea, Infinite Coxeter groups virtually surject onto $\mathbf{Z}$, Comment. Math. Helv. 72 (1997) 257 MR1470091
21	A Haefliger, Complexes of groups and orbihedra, from: "Group theory from a geometrical viewpoint (Trieste, 1990)", World Sci. Publ., River Edge, NJ (1991) 504 MR1170375
22	J E Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press (1990) MR1066460
23	M C McCord, Homotopy type comparison of a space with complexes associated with its open covers, Proc. Amer. Math. Soc. 18 (1967) 705 MR0216499
24	M Mihalik, S Tschantz, Visual Decompositions of Coxeter Groups
25	G Moussong, Hyperbolic Coxeter groups, PhD thesis, The Ohio State University, Columbus, Ohio (1988)
26	G A Niblo, L D Reeves, Coxeter groups act on $\mathrm{CAT}(0)$ cube complexes, J. Group Theory 6 (2003) 399 MR1983376
27	P Scott, T Wall, Topological methods in group theory, from: "Homological group theory (Proc. Sympos., Durham, 1977)", London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137 MR564422
28	J P Serre, Trees, Springer (1980) MR607504
29	J R Stallings, Non-positively curved triangles of groups, from: "Group theory from a geometrical viewpoint (Trieste, 1990)", World Sci. Publ., River Edge, NJ (1991) 491 MR1170374
30	J Tits, Le problème des mots dans les groupes de Coxeter, from: "Symposia Mathematica (INDAM, Rome, 1967/68) 1", Academic Press (1969) 175 MR0254129
31	Y Watatani, Property T of Kazhdan implies property FA of Serre, Math. Japon. 27 (1982) 97 MR649023