In this paper a homotopy co-momentum map (à la Callies, Frégier, Rogers and Zambon) transgressing to the standard hydrodynamical co-momentum map of Arnol’d, Marsden, 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.

在本文中，构建了超越 Arnol'd、Marsden、Weinstein 和其他人的标准流体动力学协动量图的同伦协动量图（à la Callies、Frégier、Rogers 和 Zambon），然后推广到一个特殊的黎曼方程歧管。此外，还讨论了与完美流体的欧拉演化相关的共伴轨道的协变相空间解释，特别是 Brylinski 光滑定向结的流形。作为上述同伦共动量图的应用，提供了根据多辛框架内的守恒量对（Massey）高阶连接数的重新解释，并确定了对合中第一积分的纽结理论类似物。