Abstract

Let M be a smooth manifold of dimension 2n, and let OM be the dense open subbundle in ∧² T*M of 2-covectors of maximal rank. The algebra of Diff M -invariant smooth functions of first order on OM is proved to be isomorphic to the algebra of smooth Sp(Ωx)-invariant functions on , x being a fixed point in M , and Ωx a fixed element in (OM )_x. The maximum number of functionally independent invariants is computed.

中文翻译：

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微分 2 形式的一阶不变量

摘要

令M为维数为 2 n的光滑流形，令OM为最大秩的 2-covectors 的∧ ² T * M中的密集开子束。证明了OM上一阶 Diff M 不变光滑函数的代数同构于 上的光滑Sp (Ω x ) 不变函数的代数，x是M中的不动点，Ω x是 ( OM ) _×。计算功能独立不变量的最大数量。