Open book decompositions of -manifolds

Author:
Robert Myers

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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[1]**J. W. Alexander,*A lemma on systems of knotted curves*, Proc. Nat. Acad. Sci. U.S.A.**9**(1923), 93-95.**[2]**R. H. Bing,*Necessary and sufficient conditions that a*3-*manifold be*, Ann. of Math.**68**(1958), 17-37. MR**0095471 (20:1973)****[3]**J. S. Birman,*Braids, links, and mapping class groups*, Ann. of Math. Studies, No. 82, Princeton, N.J., 1974. MR**0375281 (51:11477)****[4]**R. H. Crowell and R. H. Fox,*Introduction to knot theory*, Ginn, Boston, Mass., 1963. MR**0146828 (26:4348)****[5]**R. H. Fox,*Covering spaces with singularities*, Algebraic Geometry and Topology, Princeton Univ. Press, Princeton, N.J., 1957, pp. 243-257. MR**0123298 (23:A626)****[6]**D. L. Goldsmith,*Symmetric fibered links*, Knots, Groups, and 3-Manifolds, Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 3-23. MR**0380766 (52:1663)****[7]**F. González-Acuña, 3-*dimensional open books*, Lectures, Univ. of Iowa Topology Seminar, 1974/75.**[8]**H. M. Hilden,*Every closed orientable*3-*manifold is a*3-*fold branched covering space of*, Bull. Amer. Math. Soc.**80**(1974), 1243-1244. MR**0350719 (50:3211)****[9]**-,*Three-fold branched coverings of*, Amer. J. Math.**98**(1976), 989-998. MR**0425968 (54:13917)****[10]**H. B. Lawson,*Foliations*, Bull. Amer. Math. Soc.**80**(1974), 369-418. MR**0343289 (49:8031)****[11]**J. M. Montesinos,*A representation of closed orientable*3-*manifolds as*3-*fold branched coverings of*, Bull. Amer. Math. Soc.**80**(1974), 845-846. MR**0358784 (50:11243)****[12]**-,*Three-manifolds as*3-*fold branched covers of*, Quart. J. Math. Oxford Ser. (2)**27**(1976), 85-94. MR**0394630 (52:15431)****[13]**R. Myers,*Open book decompositions of*3-*manifolds*, Notices Amer. Math. Soc.**22**(1975), A-651.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
57M25,
57N10

Retrieve articles in all journals with MSC: 57M25, 57N10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0507346-5

Keywords:
Open book decomposition,
3-manifold,
fibered knot,
branched covering space,
braid,
foliation

Article copyright:
© Copyright 1978
American Mathematical Society