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Finiteness of mapping class groups

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We prove that the mapping class group of a non-Haken orientable irreducible 3-manifold is finite and we show that the quotient group of the mapping class group by the rotation group is virtually torsion-free if the manifold does not have 2-sphere boundary components.

Abstract

We prove that the mapping class group of a non-Haken orientable irreducible 3-manifold is finite and we show that the quotient group of the mapping class group by the rotation group is virtually torsion-free if the manifold does not have 2-sphere boundary components.

참고문헌 (18)

  1. R. Benedetti, "Lectures on Hyperbolic Geometry" (1992), Spriner Verlag
  2. M. Boileau, "Groupe des diff´eotopies de certaines vari´et´es de Seifert", C. R. Acad. Sci. Paris S´er. I Math, 303(1), pp.19~22 (1986)
  3. M. Boileau, "Scindements de Heegaard et groupe des hom´eotopies des petites vari´et´es de Seifert", Invent. Math, 106(1), pp.85~107 (1991)
  4. A. Borel, "Corners and arithmetic groups", Comment. Math. Helv, 48, pp.436~491 (1973)
  5. R. Canary, "Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups", Mem. Amer. Math. Soc, 172(812), pp.1~218 (2004)
  6. M. Culler, "Moduli of graphs and automorphisms of free groups", Invent. Math, 84(1), pp.91~119 (1986)
  7. D. Gabai, "Homotopy hyperbolic 3-manifolds are hyperbolic", Ann. of Math, 157(2), pp.335~431 (2003)
  8. V. Guirardel, "The outer space of a free product", Proc. Lond. Math. Soc, 94(3), pp.695~714 (2007)
  9. J. Hempel, "3-manifolds" (2004), American Mathematical Society
  10. W. Jaco, "Lectures on Three Manifold Topology" (1980), American Mathematical Society
  11. D. McCullough, "Topological and algebraic automorphisms of 3-manifolds, Groups of self-equivalences and related topics, In Lecture Notes in Math., 1425", pp.102~113, Springer
  12. D. McCullough, "Virtually geometrically finite mapping class groups of 3-manifolds", J. Differential Geom, 33(1), pp.1~65 (1991)
  13. D. McCullough, "Isometries of elliptic 3-manifolds", J. London Math. Soc, 65(1), pp.167~182 (2002)
  14. D. McCullough, "Three manifolds and their mappings, Lecture Notes Series" (1995), Seoul National University
  15. D. McCullough, "Homeomorphisms of 3-manifolds with compressible boundary", Mem. Amer. Math. Soc, 61(344), pp.1~100 (1986)
  16. P. Scott, "There are no fake Seifert fibre spaces with infinite π1", Ann. of Math, 117(1), pp.35~70 (1983)
  17. F. Waldhausen, "On irreducible 3-manifolds which are sufficiently large", Ann. of Math, 87, pp.56~88 (1968)
  18. F. Waldhausen, "Recent results on sufficiently large 3-manifolds, In Algebraic and geometric topology", Proc. Sympos. Pure Math., Stanford Univ., pp.21~38 (1978)

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