Generic immersions of curves, knots, monodromy and gordian number

Norbert A'Campo

Generic immersions of curves, knots, monodromy and gordian number

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arxiv math/9803081 v2 pith:VD2JZ2WG submitted 1998-03-18 math.GT

Norbert A'Campo This is my paper · ORCID

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keywords dividelinknumbergordiangenericmonodromyaddedcircle

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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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Real morsifications via the trace map
math.AG 2026-08 accept novelty 8.0 of 10

Every reduced real plane curve singularity is shown to admit a real morsification, via a new trace map built from nodal smoothings of normalization disks.

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