厄米拉格朗日空间的格拉斯曼算子上的Schubert演算
Schubert calculus on the grassmannian of hermitian lagrangian spaces
摘要：
$\mathbb{C}^n\oplus \mathbb{C}^n$中厄米拉格朗日空间的格拉斯曼算子是厄米$n\times n$矩阵空间的自然紧化。我们描述了一个舒伯特，惠特尼定期分层在这个空间，具有莫尔斯理论的起源。我们证明，这些地层定义封闭的亚解析电流LA R。Hardt，生成该空间的积分同调，我们研究了它们的交理论性质，并证明了某些奇（在K-理论意义下）的S-Porteous型定理。
英文摘要：
The grassmannian of hermitian lagrangian spaces in $\mathbb{C}^n\oplus \mathbb{C}^n$ is a natural compactification of the space of hermitian $n\times n$ matrices. We describe a Schubert-like, Whitney regular stratification on this space which has a Morse theoretic origin. We prove that these strata define closed subanalytic currents à la R. Hardt, generating the integral homology of this space, we investigate their intersection theoretic properties, and we prove certain odd (in K-theoretic sense) Thom-Porteous type theorems.
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