Some Knot Theory of Complex Plane Curves
نویسنده
چکیده
How can a complex curve be placed in a complex surface? The question is vague; many different ways to make it more specific may be imagined. The theory of deformations of complex structure, and their associated moduli spaces, is one way. Differential geometry and function theory, curvatures and currents, could be brought in. Even the generalized Nevanlinna theory of value distribution, for analytic curves, can somehow be construed as an aspect of the “placement problem”. By “knot theory” I mean to connote those aspects of the situation that are more immediately topological. I hope to show that there is something of interest there.
منابع مشابه
Knot theory of complex plane curves
The primary objects of study in the “knot theory of complex plane curves” are C-links: links (or knots) cut out of a 3-sphere in C2 by complex plane curves. There are two very different classes of C-links, transverse and totally tangential. Transverse C-links are naturally oriented. There are many natural classes of examples: links of singularities; links at infinity; links of divides, free div...
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We study the integral expression of a knot invariant obtained as the second coefficient in the perturbative expansion of Witten’s Chern-Simons path integral associated with a knot. One of the integrals involved turns out to be a generalization of the classical Crofton integral on convex plane curves and it is related with invariants of generic plane curves defined by Arnold recently with deep m...
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