Pierre Dehornoy, Ana Rechtman
Published 2019-10-08Version 1
Given a flow on a 3-dimensional integral homology sphere, we give a formula for the Euler characteristic of its transverse surfaces, in terms of boundary data only. We illustrate the formula with several examples, in particular with surfaces of low genus. 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 the helicity.
Vector fields with a given set of singular points
Homoclinic classes for generic C^1 vector fields
Singular points in generic two-parameter families of vector fields on 2-manifold
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