Geometry & Topology Volume 17, issue 4 (2013)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

A topological splitting theorem for Poincaré duality groups and high-dimensional manifolds

Aditi Kar and Graham A Niblo

Geometry & Topology 17 (2013) 2203–2221

DOI: 10.2140/gt.2013.17.2203

Bibliography

1	A Bartels, W Lück, The Borel conjecture for hyperbolic and $\mathrm{CAT}(0)$–groups, Ann. of Math. 175 (2012) 631 MR2993750
2	R Bieri, Homological dimension of discrete groups, Queen Mary College Mathematics Notes, Mathematics Department, Queen Mary College, London (1976) MR0466344
3	K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1982) MR672956
4	S E Cappell, A splitting theorem for manifolds, Invent. Math. 33 (1976) 69 MR0438359
5	M W Davis, The geometry and topology of Coxeter groups, London Mathematical Society Monographs Series 32, Princeton Univ. Press (2008) MR2360474
6	W Dicks, M J Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics 17, Cambridge Univ. Press (1989) MR1001965
7	J D Dixon, B Mortimer, Permutation groups, Graduate Texts in Mathematics 163, Springer (1996) MR1409812
8	M J Dunwoody, M E Sageev, JSJ–splittings for finitely presented groups over slender groups, Invent. Math. 135 (1999) 25 MR1664694
9	M J Dunwoody, E L Swenson, The algebraic torus theorem, Invent. Math. 140 (2000) 605 MR1760752
10	S Eilenberg, T Ganea, On the Lusternik–Schnirelmann category of abstract groups, Ann. of Math. 65 (1957) 517 MR0085510
11	J Kahn, V Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold, Ann. of Math. 175 (2012) 1127 MR2912704
12	P H Kropholler, A group-theoretic proof of the torus theorem, from: "Geometric group theory, Vol. 1" (editors G A Niblo, M Roller), London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 138 MR1238522
13	P H Kropholler, M A Roller, Splittings of Poincaré duality groups III, J. London Math. Soc. 39 (1989) 271 MR991661
14	J F Lafont, R Roy, A note on the characteristic classes of non-positively curved manifolds, Expo. Math. 25 (2007) 21 MR2286832
15	N Mok, Y T Siu, S K Yeung, Geometric superrigidity, Invent. Math. 113 (1993) 57 MR1223224
16	G A Niblo, The singularity obstruction for group splittings, Topology Appl. 119 (2002) 17 MR1881707
17	G Niblo, L Reeves, Groups acting on $\mathrm{CAT}(0)$ cube complexes, Geom. Topol. 1 (1997) 1 MR1432323
18	C D Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. 66 (1957) 1 MR0090053
19	A W Reid, A non–Haken hyperbolic 3–manifold covered by a surface bundle, Pacific J. Math. 167 (1995) 163 MR1318168
20	M Sageev, Codimension 1 subgroups and splittings of groups, J. Algebra 189 (1997) 377 MR1438181
21	P Scott, Ends of pairs of groups, J. Pure Appl. Algebra 11 (1977/78) 179 MR487104
22	P Scott, G A Swarup, Regular neighbourhoods and canonical decompositions for groups, Astérisque 289, Soc. Math. France (2003) MR2032389
23	R Strebel, A remark on subgroups of infinite index in Poincaré duality groups, Comment. Math. Helv. 52 (1977) 317 MR0457588
24	F Waldhausen, On the determination of some bounded 3–manifolds by their fundamental groups alone, from: "Proc. Internat. Sympos. on Topology and its Applications" (editor D R Kurepa) (1969) 331