Publication: Open 3-manifolds and branched coverings: a quick exposition
Full text at PDC
Advisors (or tutors)
Soc. Colombiana Mat.
This is a survey article discussing the author's work in a series of several publications on the relationship between 3-manifolds and wild knots in the 3-sphere and strings in R3 given by branched coverings. He includes an introduction to ordinary combinatorial branched coverings and a parallel introduction to the general topological branched coverings defined by R. H. Fox. Among other things one may conclude that every closed, oriented 3-manifold is a 3-fold covering of the 3-sphere branched over a wild knot. The paper ends with a brief discussion of two open problems.
Dedicado a María Teresa Lozano Imízcoz tras 27 años de fructífera colaboración
Bing, R. H. The collected papers of R. H. Bing. American Mathematical Society, Providence,1988. Ed. by Sukhjit Singh, Steve Armentrout and Robert J. Daverman, RI. xix, 1654 p. Brown, M. The monotone union of open n-cells is an open n-cell. Proc. Amer. Math. Soc. 12 (1961), 812–814. Burde, G., and Zieschang, H. Knots. Walter de Gruyter, Berlin - New York, 1985.Gruyter Studies in Mathematics, 5. Coxeter, H. S. Symmetrical definitions for the binary polyhedral groups.American Mathematical Society, Providence, 1959. Coxeter, H. S., and Moser, W. O. Generators and relations for discrete groups. Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete. Fox, R. H. A remarkable simple closed curve. Ann. of Math. 50, 2 (1949), 264–265. Fox, R. H. Algebraic Geometry and Topology. Princeton Univ. Press, Princeton, 1957, ch. Covering spaces with singularities, pp. 243–257. A Symposium in honor of S. Lefschetz. Fox, R. H. Topology of 3-manifolds and related topics. In Construction of simply connected 3-manifolds (1962), Proc. The Univ. of Georgia Institute, pp. 213–216. Prentice- Hall, Englewood Cliffs, N.J. Freudenthal, H. ¨Uber die enden diskreter r¨aume und gruppen. Comment. Math. Helv. 17 (1945), 1–38. Hilden, H. M. Every closed orientable 3-manifold is a 3-fold branched covering space of S3. Bull. Amer. Math. Soc. 80 (1974), 1243–1244.