微分几何结构模的Poincare函数
Poincare function for moduli of differential-geometric structures
摘要：
庞加莱函数是局部几何问题中计数模的一种紧凑形式。我们讨论了它的性质与V.Arnold猜想的关系，并在伪群在基上代数传递作用的情况下导出了这一猜想。然后，我们综述了微分不变式的已知计数结果，并导出了几何和分析中其他几个分类问题的新公式。
英文摘要：
The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and transitively on the base. Then we survey the known counting results for differential invariants and derive new formulae for several other classification problems in geometry and analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
