Branched covers and contact structures
HTML articles powered by AMS MathViewer
- by Jesús Gonzalo PDF
- Proc. Amer. Math. Soc. 101 (1987), 347-352 Request permission
Abstract:
The object of this paper is to prove the following Theorem. Every closed, orientable three-manifold has a parallelization by three contact forms.References
-
J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 93-95.
- Daniel Bennequin, Entrelacements et équations de Pfaff, Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982) Astérisque, vol. 107, Soc. Math. France, Paris, 1983, pp. 87–161 (French). MR 753131
- S. S. Chern, The geometry of $G$-structures, Bull. Amer. Math. Soc. 72 (1966), 167–219. MR 192436, DOI 10.1090/S0002-9904-1966-11473-8
- M. L. Gromov, Stable mappings of foliations into manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 707–734 (Russian). MR 0263103
- Hugh M. Hilden, Jose M. Montesinos, and Thomas Thickstun, Closed oriented $3$-manifolds as $3$-fold branched coverings of $S^{3}$ of special type, Pacific J. Math. 65 (1976), no. 1, 65–76. MR 420622
- W. B. R. Lickorish, A representation of orientable combinatorial $3$-manifolds, Ann. of Math. (2) 76 (1962), 531–540. MR 151948, DOI 10.2307/1970373 R. Lutz, Sur quelques propriétés des formes différentielles en dimension 3, Thesis, Strasbourg, 1971.
- Robert Lutz, Structures de contact sur les fibrés principaux en cercles de dimension trois, Ann. Inst. Fourier (Grenoble) 27 (1977), no. 3, ix, 1–15 (French, with English summary). MR 478180
- J. Martinet, Formes de contact sur les variétés de dimension $3$, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Lecture Notes in Math., Vol. 209, Springer, Berlin, 1971, pp. 142–163 (French). MR 0350771
- José María Montesinos, Lectures on $3$-fold simple coverings and $3$-manifolds, Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982) Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 157–177. MR 813111, DOI 10.1090/conm/044/813111
- W. P. Thurston and H. E. Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975), 345–347. MR 375366, DOI 10.1090/S0002-9939-1975-0375366-7
- Andrew H. Wallace, Modifications and cobounding manifolds, Canadian J. Math. 12 (1960), 503–528. MR 125588, DOI 10.4153/CJM-1960-045-7
- H. E. Winkelnkemper, Manifolds as open books, Bull. Amer. Math. Soc. 79 (1973), 45–51. MR 310912, DOI 10.1090/S0002-9904-1973-13085-X
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 347-352
- MSC: Primary 53C15; Secondary 57M12
- DOI: https://doi.org/10.1090/S0002-9939-1987-0902554-9
- MathSciNet review: 902554