Vector fields and genus in dimension 3
Dynamical Systems
2020-09-28 v2 Geometric Topology
Abstract
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.
Cite
@article{arxiv.1910.03450,
title = {Vector fields and genus in dimension 3},
author = {Pierre Dehornoy and Ana Rechtman},
journal= {arXiv preprint arXiv:1910.03450},
year = {2020}
}