A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher-order linking numbers

Antonio Michele Miti*, Mauro Spera

*Autore corrispondente per questo lavoro

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

Abstract

In this article a homotopy co-momentum map (à la Callies-Frégier-Rogers- Zambon) trangressing to the standard hydrodynamical co-momentum map of Arnol’d, Marsden and Weinstein and others is constructed and then generalized to a special class of Riemannian manifolds. Also, a covariant phase space in- terpretation of the coadjoint orbits associated to the Euler evolution for perfect fluids and in particular of Brylinski’s manifold of smooth oriented knots is discussed. As an application of the above homotopy co-momentum map, a rein- terpretation of the (Massey) higher order linking numbers in terms of conserved quantities within the multisymplectic framework is provided and knot theoretic analogues of first integrals in involution are determined.
Lingua originaleEnglish
pagine (da-a)335-354
Numero di pagine20
RivistaJournal of the Australian Mathematical Society
Volume2022
DOI
Stato di pubblicazionePubblicato - 2022

Keywords

  • Symplectic and multisymplectic geometry, homotopy co-momentum maps, hydrodynamics, higher order linking numbers.

Fingerprint

Entra nei temi di ricerca di 'A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher-order linking numbers'. Insieme formano una fingerprint unica.

Cita questo