Geodesic
AN ALTERNATE PROOF OF WISE’S MALNORMAL SPECIAL QUOTIENT THEOREM
Forum of Mathematics, Pi, Tome 4 (2016)

Voir la notice de l'article provenant de la source Cambridge University Press

We give an alternate proof of Wise’s malnormal special quotient theorem (MSQT), avoiding cubical small cancelation theory. We also show how to deduce Wise’s Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu and Wise and Haglund and Wise. 
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IAN AGOL; DANIEL GROVES; JASON FOX MANNING. AN ALTERNATE PROOF OF WISE’S MALNORMAL SPECIAL QUOTIENT THEOREM. Forum of Mathematics, Pi, Tome 4 (2016). doi: 10.1017/fmp.2015.8

[Ago13] Agol, I., ‘The virtual Haken conjecture’, Doc. Math. 18 (2013), 1045–1087. With an appendix by Agol, Daniel Groves, and Jason Manning.Google Scholar

[AGM09] Agol, I., Groves, D. and Manning, J. F., ‘Residual finiteness, QCERF and fillings of hyperbolic groups’, Geom. Topol. 13(2) (2009), 1043–1073.Google Scholar | DOI

[BC08] Baker, M. and Cooper, D., ‘A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3-manifolds’, J. Topol. 1(3) (2008), 603–642.Google Scholar

[Bas93] Bass, H., ‘Covering theory for graphs of groups’, J. Pure Appl. Algebra 89(1–2) (1993), 3–47.Google Scholar | DOI

[Bow12] Bowditch, B. H., ‘Relatively hyperbolic groups’, Internat. J. Algebra Comput. 22(3) (2012), 1250016, 66.Google Scholar

[BH99] Bridson, M. R. and Haefliger, A., ‘Metric spaces of non-positive curvature’, inGrundlehren der mathematischen Wissenschaften, Vol. 319 (Springer, Berlin, 1999).Google Scholar

[DGO11] Dahmani, F., Guirardel, V. and Osin, D., ‘Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces’, Preprint, 2011, http://front.math.ucdavis.edu/1111.7048.Google Scholar

[GMRS98] Gitik, R., Mitra, M., Rips, E. and Sageev, M., ‘Widths of subgroups’, Trans. Amer. Math. Soc. 350(1) (1998), 321–329.Google Scholar | DOI

[GM08] Groves, D. and Manning, J. F., ‘Dehn filling in relatively hyperbolic groups’, Israel J. Math. 168 (2008), 317–429.Google Scholar

[Hag08] Haglund, F., ‘Finite index subgroups of graph products’, Geom. Dedicata 135 (2008), 167–209.Google Scholar

[HW08] Haglund, F. and Wise, D. T., ‘Special cube complexes’, Geom. Funct. Anal. 17(5) (2008), 1551–1620.Google Scholar | DOI

[HW12] Haglund, F. and Wise, D. T., ‘A combination theorem for special cube complexes’, Ann. of Math. (2) 176(3) (2012), 1427–1482.Google Scholar

[Hig76] Higgins, P. J., ‘The fundamental groupoid of a graph of groups’, J. Lond. Math. Soc. (2) 13(1) (1976), 145–149.Google Scholar | DOI

[Hru10] Hruska, G. C., ‘Relative hyperbolicity and relative quasiconvexity for countable groups’, Algebr. Geom. Topol. 10(3) (2010), 1807–1856.Google Scholar

[Hru] Hruska, G. C., Erratum to: ‘Relative hyperbolicity and relative quasiconvexity for countable groups’, In preparation.Google Scholar

[HW09] Hruska, G. C. and Wise, D. T., ‘Packing subgroups in relatively hyperbolic groups’, Geom. Topol. 13(4) (2009), 1945–1988.Google Scholar

[HW15] Hsu, T. and Wise, D. T., ‘Cubulating malnormal amalgams’, Invent. Math. 199(2) (2015), 293–331.Google Scholar

[KM12] Kahn, J. and Markovic, V., ‘Immersing almost geodesic surfaces in a closed hyperbolic three manifold’, Ann. of Math. (2) 175(3) (2012), 1127–1190.Google Scholar

[Lub96] Lubotzky, A., ‘Free quotients and the first Betti number of some hyperbolic manifolds’, Transform. Groups 1(1–2) (1996), 71–82.Google Scholar

[MMP10] Manning, J. F. and Martínez-Pedroza, E., ‘Separation of relatively quasiconvex subgroups’, Pacific J. Math. 244(2) (2010), 309–334.Google Scholar

[MP12] Martínez-Pedroza, E., ‘On quasiconvexity and relatively hyperbolic structures on groups’, Geom. Dedicata 157 (2012), 269–290.Google Scholar

[Osi06] Osin, D. V., ‘Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems’, Mem. Amer. Math. Soc. 179(843) (2006), vi+100.Google Scholar

[Osi07] Osin, D. V., ‘Peripheral fillings of relatively hyperbolic groups’, Invent. Math. 167(2) (2007), 295–326.Google Scholar

[SW11] Sageev, M. and Wise, D. T., ‘Periodic flats in CAT(0) cube complexes’, Algebr. Geom. Topol. 11(3) (2011), 1793–1820.Google Scholar

[Sco78] Scott, P., ‘Subgroups of surface groups are almost geometric’, J. Lond. Math. Soc. (2) 17(3) (1978), 555–565.Google Scholar

[Ser80] Serre, J.-P., Trees, (Springer, Berlin, 1980), Translated from the French by John Stillwell.Google Scholar | DOI

[Wis12] Wise, D. T., ‘From riches to raags: 3-manifolds, right-angled Artin groups, and cubical geometry’, CBMS Regional Conference Series in Mathematics, vol. 117 (Published for the Conference Board of the Mathematical Sciences, Washington, DC, 2012).Google Scholar

[Wis] Wise, D. T., The structure of groups with a quasiconvex hierarchy, http://comet.lehman.cuny.edu/behrstock/cbms/program.html, unpublished manuscript.Google Scholar

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