A remark on the action of the mapping class group on the unit tangent bundle
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, pp. 589-601.

On montre que l’action standard du groupe modulaire Map (Σ) d’une surface Σ de genre assez grand sur le fibré unitaire tangent T 1 Σ n’est pas homotopique à une action lisse.

We prove that the standard action of the mapping class group Map (Σ) of a surface Σ of sufficiently large genus on the unit tangent bundle T 1 Σ is not homotopic to any smooth action.

DOI : 10.5802/afst.1258
Souto, J. 1

1 Department of Mathematics, University of Michigan, Ann Arbor
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Souto, J. A remark on the action of the mapping class group on the unit tangent bundle. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, pp. 589-601. doi : 10.5802/afst.1258. http://www.numdam.org/articles/10.5802/afst.1258/

[1] Bestvina (M.), Church (T.) and Souto (J.).— Some groups of mapping classes not realized by diffeomorphisms, preprint (2009).

[2] Bing (R.).— Inequivalent families of periodic homeomorphisms of E 3 , Ann. of Math. (2) 80 (1964). | MR | Zbl

[3] Casson (A.) and Bleiler (S.).— Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, 9. Cambridge University Press, 1988. | MR | Zbl

[4] Deroin (B.), Kleptsyn (V.) and Navas (A.).— Sur la dynamique unidimensionnelle en régularité intermédiaire, Acta Math. 199 (2007), no. 2. | MR | Zbl

[5] Farb (B.) and Margait (D.).— A primer on mapping class groups, to be published by Princeton University Press.

[6] Farb (B.) and Franks (J.).— Groups of homeomorphisms of one-manifolds, I: Nonlinear group actions, preprint (2001).

[7] Franks (J.) and Handel (M.).— Global fixed points for centralizers and Morita’s Theorem, Geom. Topol. 13 (2009). | MR | Zbl

[8] Korkmaz (M.).— Low-dimensional homology groups of mapping class groups: a survey, Turkish J. Math. 26 (2002). | MR | Zbl

[9] Kuusalo (T.).— Boundary mappings of geometric isomorphisms of Fuchsian groups, Ann. Acad. Sci. Fenn. Ser. A I No. 545 (1973). | MR | Zbl

[10] Marković (V.).— Realization of the mapping class group by homeomorphisms, Invent. Math. 168 (2007). | MR | Zbl

[11] Meeks (W.) and Scott (P.).— Finite group actions on 3-manifolds, Invent. Math. 86 (1986). | MR | Zbl

[12] Milnor (J.) and Stasheff (J.).— Characteristic classes, Annals of Mathematics Studies, No. 76. Princeton University Press, (1974). | MR | Zbl

[13] Morita (S.).— Characteristic classes of surface bundles, Invent. Math. 90 (1987). | MR | Zbl

[14] Neumann (W.) and Raymond (F.).— Seifert manifolds, plumbing, μ-invariant and orientation reversing maps, in Algebraic and geometric topology, Lecture Notes in Math., 664, Springer 1978. | MR | Zbl

[15] Parwani (K.).— C 1 actions on the mapping class groups on the circle, Algebr. Geom. Topol. 8 (2008). | MR | Zbl

[16] Powell (J.).— Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978). | MR | Zbl

[17] Seifert (H.).— Topologie dreidimensionalen gefaserter Räume, Acta Math. 60 (1933). | Zbl

[18] Sullivan (D.).— Hyperbolic geometry and homeomorphisms, in Proc. Georgia Topology Conf. 1977, Academic Press, 1979. | MR | Zbl

[19] Thurston (W.).— A generalization of the Reeb stability theorem, Topology 13 (1974) | MR | Zbl

[20] Waldhausen (F.).— On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968). | MR | Zbl

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