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Main Author: Lambert-Cole, Peter
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2403.05511
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author Lambert-Cole, Peter
author_facet Lambert-Cole, Peter
contents Link invariants of long pieces of orbits of a volume-preserving flow can be used to define diffeomorphism invariants of the flow. In this paper, we extend the notions of wrapping number and trunk and define invariants of links with respect to a fibration on a 3-manifold. Extending work of Dehornoy and Rechtman, we apply this to define diffeomorphism invariants wrappingness and trunkenness of volume-preserving flows on 3-manifolds and interpret these invariants as obstructions to the existence of a global surface of section for the flow. Finally, we construct flows and show that wrappingness and trunkenness are not functions of the helicity of a flow.
format Preprint
id arxiv_https___arxiv_org_abs_2403_05511
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Wrappingness and Trunkenness of Volume-Preserving Flows
Lambert-Cole, Peter
Geometric Topology
Dynamical Systems
Link invariants of long pieces of orbits of a volume-preserving flow can be used to define diffeomorphism invariants of the flow. In this paper, we extend the notions of wrapping number and trunk and define invariants of links with respect to a fibration on a 3-manifold. Extending work of Dehornoy and Rechtman, we apply this to define diffeomorphism invariants wrappingness and trunkenness of volume-preserving flows on 3-manifolds and interpret these invariants as obstructions to the existence of a global surface of section for the flow. Finally, we construct flows and show that wrappingness and trunkenness are not functions of the helicity of a flow.
title The Wrappingness and Trunkenness of Volume-Preserving Flows
topic Geometric Topology
Dynamical Systems
url https://arxiv.org/abs/2403.05511