Kodai Mathematical Journal

Surfaces in $3$-manifolds: group actions on surface bundles

Iain R. Aitchison

Full-text: Open access

Article information

Source
Kodai Math. J. Volume 17, Number 3 (1994), 549-559.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138040050

Digital Object Identifier
doi:10.2996/kmj/1138040050

Mathematical Reviews number (MathSciNet)
MR1296926

Zentralblatt MATH identifier
0847.57019

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M35: Dehn's lemma, sphere theorem, loop theorem, asphericity 57M50: Geometric structures on low-dimensional manifolds

Citation

Aitchison, Iain R. Surfaces in $3$-manifolds: group actions on surface bundles. Kodai Math. J. 17 (1994), no. 3, 549--559. doi:10.2996/kmj/1138040050. https://projecteuclid.org/euclid.kmj/1138040050.


Export citation

References

  • [ARl] I. R. Aitchison and J. H. Rubinstein, 'An introduction to polyhedral metrics of non-positive curvature on 3-manifolds', in: Geometry of Low-Dimensional Manifolds: 2 (ed. S. K. Donaldson and C. B. Thomas), London Math. Soc. Lecture Notes 151 (Cambridge University Press, Cam-bridge, 1990), pp. 127-161.
  • [AR2] I. R. Aitchison and J. H. Rubinstein, 'Canonical surgery on alternating link diagrams', in: Knot 90 (ed. A. Kawauchi), (de Gruyter, Berlin, 1992), pp. 543-558.
  • [AR3] I. R. Aitchison and J. H. Rubinstein, 'Incompressible surfaces and the topology of 3-dimensiona manifolds1, J. Austral. Math. Soc. (Series A) 55 (1993), 1-22.
  • [ALR] I. R. Aitchison, E. Lumsden and J. H. Rubinstein, 'Cusp structure of alternating links', Invent Math. 109 (1992), 473-494.
  • [Ca] A. Casson, On the Seifert fibred space conjecture', Talk at Kyoto, 1990
  • [CLR] D. Cooper, D. D. Long and A. W. Reid, 'Bundles and finite foliations', preprint, 1993
  • [Ga] D. Gabai, On 3-manifolds finitely covered by surface bundles', in: Low-Dimensional Topolog and Kleinian Groups (ed. D. B. A. Epstein), London Math. Soc. Lecture Notes 112 (Cambridge University Press, Cambridge, 1986), pp. 145-155.
  • [Ga2] D. Gabai, 'Convergence groups are Fuchsian groups', preprint
  • [GA] F. Gonzales-Acua, 'Dehn's construction on knots', Bol. Soc. Mat. Mexicana 15 (1970), 58-79
  • [Has] J. Hass, 'Surfaces minimizing area in their homology class and group actions on 3-manifolds', Math. Zeit. 199 (1988), 501-509
  • [HS] J. Hass and P. Scott, omotopy equivalence and homeomorphism of 3-manifolds', Topolog 31 (1992), 493-517.
  • [Hat] A. Hatcher, Communication via Hyam Rubinstein, Georgia, 1993
  • [Hel] J. Hempel, 3-Manifolds, Annals of Math. Studies 86 (Princeton University Press, Princeton, New Jersey, 1976)
  • [He2] J. Hempel, Orientation reversing involutions and the first Betti number for finite coverings o 3-manifolds', Invent. Math. 67 (1982), 133-142.
  • [Ja] W. Jaco, Lectures on three-manifold topology, Conf. Board of Math. Sci. 43 (American Math Society, Providence, 1980).
  • [JS] W. Jaco and P. Shalen, Seifert-fibered Spaces in 3-Manifolds, Mem. Amer. Math. Soc. 22 (1980).
  • [Joh] K. Johannson, Homotopy Equivalences of 3-manifolds with Boundary, Lecture Notes in Math ematics 761 (Springer-Verlag, Berlin 1979).
  • [Kn] H. Kneser, 'Geschlossene Flachen in dreidimensionalen Mannigfaltigkeiten', Jahresbericht de Deut. math. Verein 38 (1929), 248-260.
  • [Ko] S. Kojima, 'Isometry transformations of hyperbolic three-manifolds', Topology and its Appl 29 (1988), 297-307.
  • [Li] W. B. R. Lickorish, representation of orientable combinatorial 3-manifolds', Annals of Math 76 (1962), 531-540.
  • [Lo] D. Long, mmersions and embeddings of totally geodesic surfaces'. Bull. London Math. Soc 19 (1987), 481-484.
  • [Lu] J. Luecke, 'Finite covers of 3-manifolds containing essential tori', Trans. Amer. Math. Soc. 31 (1988), 381-391.
  • [Ma] A. A. Markov, 'Unsolvability of the problem of homeomorphy', Proc. Int. Cong. Math. (1958), 300-306
  • [Me] G. Mess, 'Centers of 3-manifold groups and groups which are coarse quasiisometric to planes', preprint
  • [Mill] J. Millson, On the first Betti number of a constant negatively curved manifold', Annals o Math. 104 (1976), 235-247.
  • [Miln] J. Milnor, unique factorisation theorem for 3-manifolds', Amer. J. Math. 84 (1962), 1-7
  • [Moi] E. Moise, ffine structures in 3-manifolds V. The triangulation theorem and Hauptvermu tung', Annals of Math. 56 (1952), 96-114.
  • [My] R. Myers, Open book decompositions of 3-manifolds', Proc. Amer. Math. Soc. 72 (1978), 397-402
  • [Pa] C. Papakyriakopoulos, On Dehn's Lemma and the asphericity of knots', Annals of Math. 6 (1957), 1-26.
  • [Pen] R. Penner, construction of pseudo-Anosov homeomorphisms', Trans. Amer. Math. Soc. 31 (1988), 179-197.
  • [Re] A. Reid, non-Haken hyperbolic 3-manifold covered by a surface bundle', preprint (1992)
  • [Sa] M. Sakuma, 'Surface bundles over S1 which are two-fold branched cyclic coverings of S3', Math Seminar Notes (Kobe) 9 (1981), 159-180.
  • [Sc] P. Scott, The geometries of 3-manifolds', Bull. London Math. Soc. 15 (1983), 401-487
  • [Sc2] P. Scott, 'Strong annulus and torus theorems and the enclosing property of characteristi submanifolds of 3-manifolds', Quart. J. Math. Oxford (2) 35 (1984), 485-506.
  • [Sol] T. Soma, 'Virtual fibers in hyperbolic 3-manifolds', Topology and its Appl. 41 (1991), 179-192
  • [So2] T. Soma, 'Virtual fibers in 3-manifold groups', J. London Math. Soc. (2) 43 (1991), 337-354
  • [St] J. Stailings, On fibering certain 3-manifolds', in: Topology of 3-Manifolds (ed. M. Fort), (Prentice-Hall, 1962), pp. 95-100
  • [Thl] W. Thurston, Lecture notes on the geometry and topology of 3-manifolds, (Princeton Univer sity, 1978).
  • [Th2] W. Thurston, 'Three dimensional manifolds, Kleinian groups and hyperbolic geometry', Bull Amer. Math. Soc. 6 (1982), 357-381.
  • [Th3] W. Thurston, 'Hyperbolic structures on 3-manifolds II: Surface groups and 3-manifolds whic fiber over the circle', unpublished preprint.
  • [Th4] W. Thurston, A norm for the homology of 3-manifolds, Memoirs of the Amer. Math. Soc. 33 (1986), 100-130.
  • [Th5] W. Thurston, On geometry and dynamics of diffeomorphismsof surfaces', Bull. Amer. Math Soc. 19 (1988), 417-^131.
  • [To] J. Tollefson, 'Periodic homeomorphisms of 3-manifolds fibered over S1', Trans. Amer. Math Soc. 223 (1976), 223-234.
  • [Wa] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large', Annals of Math. 8 (1968), 56-88.
  • [Wall] A. Wallace, 'Modifications and cobounding manifolds', Canad. J. Math. 12 (1960), 503-528