Vector Fields and Genus in Dimension 3
International Mathematics Research Notices(2020)
Abstract
Abstract Given a vector field on a 3D rational homology sphere, we give a formula for the Euler characteristic of its transverse surfaces, in terms of boundary data only. This provides a formula for the genus of a transverse surface, and in particular, of a Birkhoff section. As an application, we show that for a right-handed flow with an ergodic invariant measure, the genus is an asymptotic invariant of order 2 proportional to helicity.
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Key words
genus,fields,dimension,vector
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