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implicitly implied (by referring to a then-unpublished longer manuscript) that he had proven the conjecture for the case where the 3-manifold is closed, hyperbolic, and Haken. This was followed by a survey article in
Electronic Research Announcements in Mathematical Sciences. Several other articles
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The virtually fibered conjecture was not actually conjectured by
Thurston. Rather, he posed it as a question, writing only that "his dubious-sounding question seems to have a definite chance for a positive answer".
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for closed hyperbolic 3-manifolds . Taken together with Daniel Wise's results, this implies the virtually fibered conjecture for all closed hyperbolic 3-manifolds.
487:, Low Dimensional Topology and Kleinian Groups (ed: D.B.A. Epstein), London Mathematical Society Lecture Note Series vol 112 (1986), p. 145-155.
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The conjecture was finally settled in the affirmative in a series of papers from 2009 to 2012. In a posting on the ArXiv on 25 Aug 2009,
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is now settled, the only case needed to be proven for the virtually fibered conjecture is that of hyperbolic 3-manifolds.
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have followed, including the aforementioned longer manuscript by Wise. In March 2012, during a conference at
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The original interest in the virtually fibered conjecture (as well as its weaker cousins, such as the
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Christopher Hruska, G. C.; Wise, Daniel T. (2014). "Finiteness properties of cubulated groups".
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Bergeron, Nicolas; Wise, Daniel T. (2012). "A boundary criterion for cubulation".
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106:) stemmed from the fact that any of these conjectures, combined with Thurston's
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231:"Research announcement: The structure of groups with a quasiconvex hierarchy"
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415:. With an appendix by Ian Agol, Daniel Groves and Jason Manning: 1045–1087.
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542:"Getting Into Shapes: From Hyperbolic Geometry to Cube Complexes and Back"
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449:"Three dimensional manifolds, Kleinian groups and hyperbolic geometry"
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Hsu, Tim; Wise, Daniel T. (2015). "Cubulating malnormal amalgams".
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Conjecture pertaining to finite covers of 3-manifold subfields
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Electronic
Research Announcements in Mathematical Sciences
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A 3-manifold which has such a finite cover is said to
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The structure of groups with a quasiconvex hierarchy
491:Agol, Ian (2008). "Criteria for virtual fibering".
264:"A combination theorem for special cube complexes"
91:The hypotheses of the conjecture are satisfied by
88:) Euler characteristic of the base space is zero.
485:On 3-manifold finitely covered by surface bundles
453:Bulletin of the American Mathematical Society
80:virtually fibers if and only if the rational
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262:Haglund, Frédéric; Wise, Daniel (2012).
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84:of the Seifert fibration or the (
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476:10.1090/S0273-0979-1982-15003-0
186:American Journal of Mathematics
405:"The virtual Haken conjecture"
59:surface bundle over the circle
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447:Thurston, William P. (1982).
130:announced he could prove the
25:virtually fibered conjecture
281:10.4007/annals.2012.176.3.2
149:Surface subgroup conjecture
95:. In fact, given that the
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144:Virtually Haken conjecture
132:virtually Haken conjecture
104:virtually Haken conjecture
362:10.1007/s00222-014-0513-4
319:10.1112/S0010437X13007112
97:geometrization conjecture
49:3-manifold with infinite
342:Inventiones Mathematicae
124:Institut Henri Poincaré
108:hyperbolization theorem
297:Compositio Mathematica
248:10.3934/era.2009.16.44
93:hyperbolic 3-manifolds
515:10.1112/jtopol/jtn003
409:Documenta Mathematica
268:Annals of Mathematics
229:Wise, Daniel (2009).
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154:Ehrenpreis conjecture
37:, states that every
493:Journal of Topology
354:2015InMat.199..293H
74:Seifert fiber space
403:Agol, Ian (2013).
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540:(2012-10-02).
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570:Conjectures
565:3-manifolds
119:Daniel Wise
57:which is a
43:irreducible
21:3-manifolds
559:Categories
483:D. Gabai,
441:References
126:in Paris,
506:0707.4522
461:CiteSeerX
422:1204.2810
370:122292998
327:119341019
310:1209.1074
241:: 44–55.
199:0908.3609
47:atoroidal
138:See also
128:Ian Agol
86:orbifold
29:American
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431:3104553
350:Bibcode
216:2931226
76:, then
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68:. If
39:closed
23:, the
519:S2CID
501:arXiv
417:arXiv
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323:S2CID
305:arXiv
194:arXiv
160:Notes
72:is a
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