2024/03/08 by Peter Lambert‐Cole, Lambert-Cole, Peter
Chemical Engineering · Engineering · #Dynamical Systems (math.DS) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Topology (math.GT) #Lattice Boltzmann Simulation Studies #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.2403.05511
openalex publication_date 2024/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.