Open book decompositions of $3$-manifolds
HTML articles powered by AMS MathViewer
- by Robert Myers
- Proc. Amer. Math. Soc. 72 (1978), 397-402
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507346-5
- PDF | Request permission
Abstract:
We prove that every closed, orientable 3-manifold has an open book decomposition with connected binding. We then give some applications of this result.References
- J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 93-95.
- R. H. Bing, Necessary and sufficient conditions that a $3$-manifold be $S^{3}$, Ann. of Math. (2) 68 (1958), 17–37. MR 95471, DOI 10.2307/1970041
- Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
- Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Ginn and Company, Boston, Mass., 1963. Based upon lectures given at Haverford College under the Philips Lecture Program. MR 0146828
- Ralph H. Fox, Covering spaces with singularities, Algebraic geometry and topology. A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N.J., 1957, pp. 243–257. MR 0123298
- Deborah L. Goldsmith, Symmetric fibered links, Knots, groups, and $3$-manifolds (Papers dedicated to the memory of R. H. Fox), Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 3–23. MR 0380766 F. González-Acuña, 3-dimensional open books, Lectures, Univ. of Iowa Topology Seminar, 1974/75.
- Hugh M. Hilden, Every closed orientable $3$-manifold is a $3$-fold branched covering space of $S^{3}$, Bull. Amer. Math. Soc. 80 (1974), 1243–1244. MR 350719, DOI 10.1090/S0002-9904-1974-13699-2
- Hugh M. Hilden, Three-fold branched coverings of $S^{3}$, Amer. J. Math. 98 (1976), no. 4, 989–997. MR 425968, DOI 10.2307/2374037
- H. Blaine Lawson Jr., Foliations, Bull. Amer. Math. Soc. 80 (1974), 369–418. MR 343289, DOI 10.1090/S0002-9904-1974-13432-4
- José M. Montesinos, A representation of closed orientable $3$-manifolds as $3$-fold branched coverings of $S^{3}$, Bull. Amer. Math. Soc. 80 (1974), 845–846. MR 358784, DOI 10.1090/S0002-9904-1974-13535-4
- José M. Montesinos, Three-manifolds as $3$-fold branched covers of $S^{3}$, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94. MR 394630, DOI 10.1093/qmath/27.1.85 R. Myers, Open book decompositions of 3-manifolds, Notices Amer. Math. Soc. 22 (1975), A-651.
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 397-402
- MSC: Primary 57M25; Secondary 57N10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507346-5
- MathSciNet review: 507346