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2019-01-22  00:53 hrs.

Some knot theory of complex hypersurfaces

Lee Rudolph
Clark University


In 1928, Brauner became the first to apply knot theory to the understanding of singular points of complex plane curves. In 1968, Milnor considerably extended the subject with his pioneering study of the topology of isolated singular points of complex hypersurfaces in all dimensions. Since then much progress has been made on this local theory; but little has been published on related larger-scale phenomena, except in complex dimension 2 where various tools and techniques (quasipositivity, the enhanced Milnor number, contact and symplectic geometry and topology, etc) have led to deeper though far from complete understanding. I will describe some old and many new (or not previously published) results in higher dimensions, and pose a number of open questions--both general and specific--for future work.




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