Polynomial invariants for fibered 3-manifolds and teichmüller geodesics for foliations
McMullen, Curtis T.
Annales scientifiques de l'École Normale Supérieure, Tome 33 (2000), p. 519-560 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_2000_4_33_4_519_0,
     author = {McMullen, Curtis T.},
     title = {Polynomial invariants for fibered 3-manifolds and teichm\"uller geodesics for foliations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {33},
     year = {2000},
     pages = {519-560},
     doi = {10.1016/s0012-9593(00)00121-x},
     mrnumber = {2002d:57015},
     zbl = {01702167},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2000_4_33_4_519_0}
}

McMullen, Curtis T. Polynomial invariants for fibered 3-manifolds and teichmüller geodesics for foliations. Annales scientifiques de l'École Normale Supérieure, Tome 33 (2000) pp. 519-560. doi : 10.1016/s0012-9593(00)00121-x. http://gdmltest.u-ga.fr/item/ASENS_2000_4_33_4_519_0/

[1] Arnoux P., Yoccoz J.-C., Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris 292 (1981) 75-78. | MR 82b:57018 | Zbl 0478.58023

[2] Atiyah M., Macdonald I., Commutative Algebra, Addison-Wesley, 1969. | MR 39 #4129

[3] Bauer M., An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361-370. | MR 92g:57024 | Zbl 0754.57007

[4] Bers L., An extremal problem for quasiconformal maps and a theorem by Thurston, Acta Math. 141 (1978) 73-98. | MR 57 #16704 | Zbl 0389.30018

[5] Bestvina M., Handel M., Train-tracks for surface homeomorphisms, Topology 34 (1995) 109-140. | MR 96d:57014 | Zbl 0837.57010

[6] Birman J.S., Braids, Links and Mapping-Class Groups, Annals of Math. Studies, Vol. 82, Princeton University Press, 1974. | MR 51 #11477 | Zbl 0305.57013

[7] Bonahon F., Geodesic laminations with transverse Hölder distributions, Ann. Sci. École Norm. Sup. 30 (1997) 205-240. | Numdam | MR 98b:57027 | Zbl 0887.57018

[8] Bonahon F., Transverse Hölder distributions for geodesic laminations, Topology 36 (1997) 103-122. | MR 97j:57015 | Zbl 0871.57027

[9] Brinkman P., An implementation of the Bestvina-Handel algorithm for surface homeomorphisms, J. Exp. Math., to appear. | Zbl 0982.57005

[10] Burde G., Zieschang H., Knots, Walter de Gruyter & Co., 1985. | MR 87b:57004 | Zbl 0568.57001

[11] Cantwell J., Conlon L., Isotopies of foliated 3-manifolds without holonomy, Adv. Math. 144 (1999) 13-49. | MR 2000c:57060 | Zbl 0934.57033

[12] Connes A., Noncommutative Geometry, Academic Press, 1994. | MR 95j:46063 | Zbl 0818.46076

[13] Cooper D., Long D.D., Reid A.W., Finite foliations and similarity interval exchange maps, Topology 36 (1997) 209-227. | MR 97j:57032 | Zbl 0873.57023

[14] Dunfield N., Alexander and Thurston norms of fibered 3-manifolds, Preprint, 1999.

[15] Fathi A., Démonstration d'un théorème de Penner sur la composition des twists de Dehn, Bull. Sci. Math. France 120 (1992) 467-484. | Numdam | MR 93j:57005 | Zbl 0779.57005

[16] Fathi A., Laudenbach F., Poénaru V., Travaux de Thurston sur les Surfaces, Astérisque, Vol. 66-67, 1979. | MR 82m:57003

[17] Fried D., Fibrations over S1 with pseudo-Anosov monodromy, in : Travaux de Thurston sur les Surfaces, Astérisque, Vol. 66-67, 1979, pp. 251-265. | Zbl 0446.57023

[18] Fried D., Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helvetici 57 (1982) 237-259. | MR 84g:58083 | Zbl 0503.58026

[19] Fried D., The geometry of cross sections to flows, Topology 21 (1982) 353-371. | MR 84d:58068 | Zbl 0594.58041

[20] Fried D., Growth rate of surface homeomorphisms and flow equivalence, Ergod. Theory Dynamical Syst. 5 (1985) 539-564. | MR 88f:58118 | Zbl 0603.58020

[21] Gabai D., Foliations and the topology of 3-manifolds, J. Differential Geom. 18 (1983) 445-503. | MR 86a:57009 | Zbl 0533.57013

[22] Gabai D., Foliations and genera of links, Topology 23 (1984) 381-394. | MR 86h:57006 | Zbl 0567.57021

[23] Gantmacher F.R., The Theory of Matrices, Vol. II, Chelsea, New York, 1959.

[24] Harer J.L., Penner R.C., Combinatorics of Train Tracks, Annals of Math. Studies, Vol. 125, Princeton University Press, 1992. | MR 94b:57018 | Zbl 0765.57001

[25] Hatcher A., Oertel U., Affine lamination spaces for surfaces, Pacific J. Math. 154 (1992) 87-101. | MR 93b:57033 | Zbl 0772.57032

[26] Hubbard J., Masur H., Quadratic differentials and foliations, Acta Math. 142 (1979) 221-274. | MR 80h:30047 | Zbl 0415.30038

[27] Kronheimer P., Mrowka T., Scalar curvature and the Thurston norm, Math. Res. Lett. 4 (1997) 931-937. | MR 98m:57039 | Zbl 0892.57011

[28] Lang S., Algebra, Addison-Wesley, 1984. | Zbl 0712.00001

[29] Laudenbach F., Blank S., Isotopie de formes fermées en dimension trois, Invent. Math. 54 (1979) 103-177. | MR 81d:58003 | Zbl 0435.58002

[30] Lind D., Marcus B., An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995. | MR 97a:58050 | Zbl 00822672

[31] Long D., Oertel U., Hyperbolic surface bundles over the circle, in : Progress in Knot Theory and Related Topics, Travaux en Cours, Vol. 56, Hermann, 1997, pp. 121-142. | MR 98m:57022 | Zbl 0959.57019

[32] Matsumoto S., Topological entropy and Thurston's norm of atoroidal surface bundles over the circle, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987) 763-778. | MR 89c:57011 | Zbl 0647.57006

[33] Mcmullen C., The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology, Preprint, 1998.

[34] Mosher L., Surfaces and branched surfaces transverse to pseudo-Anosov flows on 3-manifolds, J. Differential Geom. 34 (1991) 1-36. | MR 92k:57029 | Zbl 0754.58031

[35] Ngô V.Q., Roussarie R., Sur l'isotopie des formes fermées en dimension 3, Invent. Math. 64 (1981) 69-87. | MR 83b:58006 | Zbl 0467.58004

[36] Northcott D.G., Finite Free Resolutions, Cambridge University Press, 1976. | MR 57 #377 | Zbl 0328.13010

[37] Oertel U., Homology branched surfaces : Thurston's norm on H2(M³), in : Epstein D.B. (Ed.), Low-Dimensional Topology and Kleinian Groups, Cambridge Univ. Press, 1986, pp. 253-272. | MR 89e:57011 | Zbl 0628.57011

[38] Oertel U., Affine laminations and their stretch factors, Pacific J. Math. 182 (1998) 303-328. | MR 99i:57037 | Zbl 0909.57008

[39] Penner R., A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179-198. | MR 89k:57026 | Zbl 0706.57008

[40] Penner R., Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443-450. | MR 91m:57010 | Zbl 0726.57013

[41] Rolfsen D., Knots and Links, Publish or Perish, Inc., 1976. | MR 58 #24236 | Zbl 0339.55004

[42] Thurston W.P., Geometry and Topology of Three-Manifolds, Lecture Notes, Princeton University, 1979.

[43] Thurston W.P., A norm for the homology of 3-manifolds, Mem. Amer. Math. Soc. 339 (1986) 99-130. | MR 88h:57014 | Zbl 0585.57006

[44] Thurston W.P., On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417-432. | MR 89k:57023 | Zbl 0674.57008

[45] Thurston W.P., Three-manifolds, foliations and circles, I, Preprint, 1997.

[46] Yoccoz J.-C., Petits Diviseurs en Dimension 1, Astérisque, Vol. 231, 1995. | MR 96f:58005 | Zbl 0836.30001

[47] Zhirov A. Yu., On the minimum dilation of pseudo-Anosov diffeomorphisms of a double torus, Uspekhi Mat. Nauk 50 (1995) 197-198. | MR 96e:58123 | Zbl 0847.58057