伪群作用的不变量：同调方法和不变性定理
Invariants of pseudogroup actions: Homological methods and Finiteness theorem
摘要：
研究了子流形关于可迁伪群作用的等价问题。相应的微分不变式通过形式理论确定，并导致k-变量和k-协变量的概念，即使在不可积的伪群的情况下。他们的计算是基于上同调的机器：我们介绍了一个复杂的协变，定义他们的上同调，并证明有限性定理。这隐含了著名的关于微分不变式的Lie-Tresse定理。我们也将这个定理推广到微分方程的伪群作用的情形。
英文摘要：
We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of k-variants and k-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology and prove the finiteness theorem. This implies the well-known Lie-Tresse theorem about differential invariants. We also generalize this theorem to the case of pseudogroup action on differential equations.
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