Generic immersions of curves, knots, monodromy and gordian number

Details Generic immersions of curves, knots, monodromy and gordian number Generic immersions of curves, knots, monodromy and gordian number

1998-03-18

arxiv.org/abs/math/9803081v2

Inst. Hautes Etudes Sci. Publ. Math. No. 88 (1998), 151-169 (1999)

Mathematics

Geometric Topology

tex, 17 pages, 7 figures

Scientific paper

Starting from a divide, i.e. a generic immersion of finitely many copies of the interval [0,1] in the disk, we construct a classical link in the 3-sphere. We prove that the link's complement fibers over the circle, if the divide is connected. Moreover, we compute the monodromy diffeomorphism from the combinatorics of the divide. We added to this version of the paper the theorem about the gordian number of the link of a divide. The gordian number of the link of a divide equals the number of double points of the divide.

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