论文标题
多项式的空间是作为浸入式和嵌入的硕士
Spaces of polynomials as Grassmanians for immersions and embeddings
论文作者
论文摘要
令$ y $为平滑的紧凑型$ n $ manifold。我们研究了平滑的嵌入和沉浸式$β：m \至\ mathbb r \ times y $ compact $ n $ -manifolds $ m $ $ m $，使$β（m）$避免了一些封闭的封闭式poset $θ$ of {\ sf cantent cantent patterns} to poffectious y mathip y math y math y math y math y math y math y math。然后，对于固定的$ y $，我们引入了这种$β$之间的等价关系；它是伪异构和伴侣之间的交叉。我们称此关系{\ sf Quasitopy}。在对准pies的研究中，空间$ \ MATHCAL P_D^{\ MATHBFcθ} $与真实的分隔线的$ d $的真实单变量多项式相关，其组合图案避免了给定的封闭poset $θ$，扮演格拉马主义者的经典角色。 We compute the quasitopy classes $\mathcal{QT}_d^{\mathsf{emb}}(Y, \mathbf cΘ)$ of $Θ$-constrained embeddings $β$ in terms of homotopy/homology theory of spaces $Y$ and $\mathcal P_d^{\mathbf cΘ}$.我们还证明，emeddings的准序列稳定为$ d \ to \ infty $。
Let $Y$ be a smooth compact $n$-manifold. We study smooth embeddings and immersions $β: M \to \mathbb R \times Y$ of compact $n$-manifolds $M$ such that $β(M)$ avoids some a priory chosen closed poset $Θ$ of {\sf tangent patterns} to the fibers of the obvious projection $π: \mathbb R \times Y \to Y$. Then, for a fixed $Y$, we introduce an equivalence relation between such $β$'s; it is a crossover between pseudo-isotopies and bordisms. We call this relation {\sf quasitopy}. In the study of quasitopies, the spaces $\mathcal P_d^{\mathbf cΘ}$ of real univariate polynomials of degree $d$ with real divisors, whose combinatorial patterns avoid a given closed poset $Θ$, play the classical role of Grassmanians. We compute the quasitopy classes $\mathcal{QT}_d^{\mathsf{emb}}(Y, \mathbf cΘ)$ of $Θ$-constrained embeddings $β$ in terms of homotopy/homology theory of spaces $Y$ and $\mathcal P_d^{\mathbf cΘ}$. We prove also that the quasitopies of emeddings stabilize, as $d \to \infty$.
