论文标题
多项式的空间，分隔线有限，作为遍历流量的硕士
Spaces of polynomials with constrained divisors as Grassmanians for traversing flows
论文作者
论文摘要
我们研究{\ sf traversing} vector flow $ v $在平滑紧凑型歧管上$ x $带边界。对于给定的紧凑型歧管$ \ hat x $，配备了一个穿越的矢量字段$ \ hat v $，与$ \ partial \ hat x $相对于{\ sf convex} $ \ hat v $ -trajectory的图案$θ$。特别是，对于每个$ \ hat v $ -trajectory $ \hatγ$，我们限制了$ \hatγ\capα（\ partial x）$的基数，均匀数字$ d $。我们称$（\ hat x，\ hat v）$ a {\ sf convex pseudo-exparive/emplenp}的$（x，v）$。在这里，矢量字段$ v =α^\匕首（\ hat v）$是$α$ - $ \ hat v $ to $ x $的$α$转移。 对于固定的$（\ hat x，\ hat v）$，我们在凸成pseudo-reveapers/ endevels $α中引入了等价关系：（ x，x，v）\ to（\ hat x，\ hat v）$，我们称之为{\ sf sf quasitopy}。准概念的概念是伪开发与它们的伪异构体之间的跨界。 In the study of quasitopies $\mathcal{QT}_d(Y, \mathbf cΘ)$, the spaces $\mathcal P_d^{\mathbf cΘ}$ of real univariate polynomials of degree $d$ with real divisors whose combinatorial types avoid the closed poset $Θ$ play the classical role of Grassmanians. 我们用涉及$（\ hat x，\ hat v）$和$ \ MATHCAL P_D^{\ MATHBFcθ} $的同句理论术语计算，这是避免$θ$ - tangengency模式的凸信封的准论。我们介绍了伪开发的特征类别，并表明它们是他们的绝对类别的不变性。然后，我们证明了Quasitopies $ \ MATHCAL {QT} _D（y，\ \ Mathbfcθ）$经常稳定为$ d \ to \ infty $。
We study {\sf traversing} vector flows $v$ on smooth compact manifolds $X$ with boundary. For a given compact manifold $\hat X$, equipped with a traversing vector field $\hat v$ which is {\sf convex} with respect to $\partial\hat X$, we consider submersions/embeddings $α: X \to \hat X$ such that $\dim X = \dim \hat X$ and $α(\partial X)$ avoids a priory chosen tangency patterns $Θ$ to the $\hat v$-trajectories. In particular, for each $\hat v$-trajectory $\hatγ$, we restrict the cardinality of $\hatγ\cap α(\partial X)$ by an even number $d$. We call $(\hat X, \hat v)$ a {\sf convex pseudo-envelop/envelop} of the pair $(X, v)$. Here the vector field $v = α^\dagger(\hat v)$ is the $α$-transfer of $\hat v$ to $X$. For a fixed $(\hat X, \hat v)$, we introduce an equivalence relation among convex pseudo-envelops/ envelops $α: (X, v) \to (\hat X, \hat v)$, which we call a {\sf quasitopy}. The notion of quasitopy is a crossover between bordisms of pseudo-envelops and their pseudo-isotopies. In the study of quasitopies $\mathcal{QT}_d(Y, \mathbf cΘ)$, the spaces $\mathcal P_d^{\mathbf cΘ}$ of real univariate polynomials of degree $d$ with real divisors whose combinatorial types avoid the closed poset $Θ$ play the classical role of Grassmanians. We compute, in the homotopy-theoretical terms that involve $(\hat X, \hat v)$ and $\mathcal P_d^{\mathbf cΘ}$, the quasitopies of convex envelops which avoid the $Θ$-tangency patterns. We introduce characteristic classes of pseudo-envelops and show that they are invariants of their quasitopy classes. Then we prove that the quasitopies $\mathcal{QT}_d(Y, \mathbf cΘ)$ often stabilize, as $d \to \infty$.
