Vector Fields and Genus in Dimension 3
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Publication:5862778
DOI10.1093/IMRN/RNAA255zbMath1498.57027arXiv1910.03450OpenAlexW3089166488MaRDI QIDQ5862778
Publication date: 10 March 2022
Published in: Unnamed Author (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1910.03450
Vector fields, frame fields in differential topology (57R25) Dynamics induced by flows and semiflows (37C10) Low-dimensional dynamical systems (37E99)
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