A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866917060080041984 |
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| author | Miti, Antonio Michele Spera, Mauro |
| author_facet | Miti, Antonio Michele Spera, Mauro |
| contents | 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 interpretation 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 reinterpretation 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1805_01696 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers Miti, Antonio Michele Spera, Mauro Differential Geometry Symplectic Geometry 58D10, 53D20, 55S30, 57M25, 76B47 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 interpretation 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 reinterpretation 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. |
| title | A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers |
| topic | Differential Geometry Symplectic Geometry 58D10, 53D20, 55S30, 57M25, 76B47 |
| url | https://arxiv.org/abs/1805.01696 |