Geodesic
Regular neighbourhoods and canonical decompositions for groups
Scott, Peter1 ; Swarup, Gadde2
1 Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA
2 Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
Electronic research announcements of the American Mathematical Society, Tome 08 (2002), pp. 20-28.

Voir la notice de l'article provenant de la source American Mathematical Society

We find canonical decompositions for finitely presented groups which essentially specialise to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under automorphisms of the group. A crucial new ingredient is the concept of a regular neighbourhood of a family of almost invariant subsets of a group. An almost invariant set is an analogue of an immersion.
DOI : 10.1090/S1079-6762-02-00102-6

Scott, Peter 1 ; Swarup, Gadde 2

1 Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA
2 Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia 
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Scott, Peter; Swarup, Gadde. Regular neighbourhoods and canonical decompositions for groups. Electronic research announcements of the American Mathematical Society, Tome 08 (2002), pp. 20-28. doi : 10.1090/S1079-6762-02-00102-6. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-02-00102-6/

[1] Bestvina, Mladen, Feighn, Mark Bounding the complexity of simplicial group actions on trees Invent. Math. 1991 449 469

[2] Bowditch, Brian H. Cut points and canonical splittings of hyperbolic groups Acta Math. 1998 145 186

[3] Dunwoody, M. J., Roller, M. A. Splitting groups over polycyclic-by-finite subgroups Bull. London Math. Soc. 1993 29 36

[4] Dunwoody, M. J., Sageev, M. E. JSJ-splittings for finitely presented groups over slender groups Invent. Math. 1999 25 44

[5] Dunwoody, M. J., Swenson, E. L. The algebraic torus theorem Invent. Math. 2000 605 637

[6] Freedman, Michael, Hass, Joel, Scott, Peter Least area incompressible surfaces in 3-manifolds Invent. Math. 1983 609 642

[7] Jaco, William H., Shalen, Peter B. Seifert fibered spaces in 3-manifolds Mem. Amer. Math. Soc. 1979

[8] Johannson, Klaus Homotopy equivalences of 3-manifolds with boundaries 1979

[9] Kropholler, P. H. An analogue of the torus decomposition theorem for certain Poincaré duality groups Proc. London Math. Soc. (3) 1990 503 529

[10] Mess, Geoffrey Examples of Poincaré duality groups Proc. Amer. Math. Soc. 1990 1145 1146

[11] Rips, E., Sela, Z. Cyclic splittings of finitely presented groups and the canonical JSJ decomposition Ann. of Math. (2) 1997 53 109

[12] Graves, Lawrence M. The Weierstrass condition for multiple integral variation problems Duke Math. J. 1939 656 660

[13] Scott, Peter, Swarup, Gadde A. Splittings of groups and intersection numbers Geom. Topol. 2000 179 218

[14] Scott, G. P., Swarup, G. A. An algebraic annulus theorem Pacific J. Math. 2000 461 506

[15] Scott, Peter, Swarup, Gadde A. Canonical splittings of groups and 3-manifolds Trans. Amer. Math. Soc. 2001 4973 5001

[16] Sela, Z. Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups. II Geom. Funct. Anal. 1997 561 593

[17] Proceedings of the International Symposium on Topology and its Applications, Herceg-Novi, 25–31. 8. 1968, Yugoslavia 1969 356

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