Solid angles, magnetic fields and Seifert hypersurfaces

Speaker(s)

Maciej Borodzik

Affiliation

Uniwersytet Warszawski / IMPAN

Date

April 8, 2016, 10:15 a.m.

Room

room 5840

Seminar

Seminar of Dynamical Systems Group

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Given a knot K in R^3 we define a function F that assigns to a point x away of K the solid angle of a surface spanned by K. This is closely related to a scalar magnetic potential of a field induced by the magnetic current on K. It turns out that F is locally a fibration near K and the inverse images of non-critical values are Seifert surfaces for K. This analytic construction can be carried through in higher dimensions giving an explicit analytic construction of a Seifert hypersurface for general codimension 2 embeddings. Joint project with S. Dangskul (Edinburgh).

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