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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Hughes, Mark C 2016. Braiding link cobordisms and non-ribbon surfaces. Algebraic & Geometric Topology, Vol. 15, Issue. 6, p. 3707.


    Kamada, Seiichi 2007. Graphic descriptions of monodromy representations. Topology and its Applications, Vol. 154, Issue. 7, p. 1430.


    Kamada, Seiichi and Matsumoto, Yukio 2005. Word representation of cords on a punctured plane. Topology and its Applications, Vol. 146-147, p. 21.


    Kamada, Seiichi and Matsumoto, Yukio 2005. Enveloping monoidal quandles. Topology and its Applications, Vol. 146-147, p. 133.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 120, Issue 2
  • August 1996, pp. 237-245

On braid monodromies of non-simple braided surfaces

  • Seiichi Kamada (a1)
  • DOI: http://dx.doi.org/10.1017/S030500410007482X
  • Published online: 24 October 2008
Abstract

A braided surface of degree m is a compact oriented surface S embedded in a bidisk such that is a branched covering map of degree m and , where is the projection. It was defined L. Rudolph [14, 16] with some applications to knot theory, cf. [13, 14, 15, 16, 17, 18]. A similar notion was defined O. Ya. Viro: A (closed) 2-dimensional braid in R4 is a closed oriented surface F embedded in R4 such that and pr2F: FS2 is a branched covering map, where is the tubular neighbourhood of a standard 2-sphere in R4. It is related to 2-knot theory, cf. [8, 9, 10]. Braided surfaces and 2-dimensional braids are called simple if their associated branched covering maps are simple. Simple braided surfaces and simple 2-dimensional braids are investigated in some articles, [5, 8, 9, 14, 16], etc. This paper treats of non-simple braided surfaces in the piecewise linear category. For braided surfaces a natural weak equivalence relation, called braid ambient isotopy, appears essentially although it is not important for classical dimensionai braids Artin's argument [1].

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[1]E. Artin . Theory of braids. Ann. of Math. 48 (1947), 101126.

[2]I. Berstein and A. L. Edmonds . On the construction of branched coverings of low-dimensional manifolds. Trans. Amer. Math. Soc. 247 (1979), 87124.

[6]A. L. Edmonds , R. S. Kulkarni and R. E. Stong . Realizability of branched coverings of surfaces. Trans. Amer. Math. Soc. 282 (1984), 773790.

[7]T. Fiedler . A small state sum for knots. Topology 32 (1993), 281294.

[8]S. Kamada . Surfaces in R4 of braid index three are ribbon. J. Knot Theory Ramifications 1 (1992), 137160.

[9]S. Kamada . A characterization of groups of closed orientable surfaces in 4-space. Topology 33 (1994), 113122.

[10]S. Kamada . Alexander's and Markov's theorems in dimension four. Bull. Amer. Math. Soc. 31 (1994), 6467.

[13]L. Rudolph . Algebraic functions and closed braids. Topology 22 (1983), 191202.

[14]L. Rudolph . Braided surfaces and Seifert ribbons for closed braids. Comment. Math. Helv. 58 (1983), 137.

[15]L. Rudolph . Some topologically locally-flat surfaces in the complex projectives plane. Comment. Math. Helv. 59 (1984), 592599.

[17]L. Rudolph . A characterization of quasipositive Seifert surfaces (Constructions of quasipositive knots and links, III). Topology 31 (1992), 231237.

[18]L. Rudolph . Quasipositivity as an obstruction to sliceness. Bull. Amer. Math. Soc. 29 (1993), 5159.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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