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AN ALTERNATE PROOF OF WISE’S MALNORMAL SPECIAL QUOTIENT THEOREM

  • IAN AGOL (a1), DANIEL GROVES (a2) and JASON FOX MANNING (a3)
Abstract

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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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. Baker  and D. Cooper , ‘A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3-manifolds’, J. Topol. 1(3) (2008), 603642.

H. Bass , ‘Covering theory for graphs of groups’, J. Pure Appl. Algebra 89(1–2) (1993), 347.

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

R. Gitik , M. Mitra , E. Rips  and M. Sageev , ‘Widths of subgroups’, Trans. Amer. Math. Soc. 350(1) (1998), 321329.

F. Haglund  and D. T. Wise , ‘Special cube complexes’, Geom. Funct. Anal. 17(5) (2008), 15511620.

F. Haglund  and D. T. Wise , ‘A combination theorem for special cube complexes’, Ann. of Math. (2) 176(3) (2012), 14271482.

G. C. Hruska , ‘Relative hyperbolicity and relative quasiconvexity for countable groups’, Algebr. Geom. Topol. 10(3) (2010), 18071856.

T. Hsu  and D. T. Wise , ‘Cubulating malnormal amalgams’, Invent. Math. 199(2) (2015), 293331.

J. Kahn  and V. Markovic , ‘Immersing almost geodesic surfaces in a closed hyperbolic three manifold’, Ann. of Math. (2) 175(3) (2012), 11271190.

A. Lubotzky , ‘Free quotients and the first Betti number of some hyperbolic manifolds’, Transform. Groups 1(1–2) (1996), 7182.

J. F. Manning  and E. Martínez-Pedroza , ‘Separation of relatively quasiconvex subgroups’, Pacific J. Math. 244(2) (2010), 309334.

E. Martínez-Pedroza , ‘On quasiconvexity and relatively hyperbolic structures on groups’, Geom. Dedicata 157 (2012), 269290.

D. V. Osin , ‘Peripheral fillings of relatively hyperbolic groups’, Invent. Math. 167(2) (2007), 295326.

M. Sageev  and D. T. Wise , ‘Periodic flats in CAT(0) cube complexes’, Algebr. Geom. Topol. 11(3) (2011), 17931820.

J.-P. Serre , Trees, (Springer, Berlin, 1980), Translated from the French by John Stillwell.

D. T. Wise , ‘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).

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Forum of Mathematics, Pi
  • ISSN: -
  • EISSN: 2050-5086
  • URL: /core/journals/forum-of-mathematics-pi
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