Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spaces of polynomials with constrained divisors as Grassmanians for
  traversing flows   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 $\alpha: X \to \hat X$
such that $\dim X = \dim \hat X$ and $\alpha(\partial X)$ avoids a priory
chosen tangency patterns $\Theta$ to the $\hat v$-trajectories. In particular,
for each $\hat v$-trajectory $\hat\gamma$, we restrict the cardinality of
$\hat\gamma \cap \alpha(\partial X)$ 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 $v = \alpha^\dagger(\hat v)$ is the $\alpha$-transfer of $\hat v$
to $X$.
  For a fixed $(\hat X, \hat v)$, we introduce an equivalence relation among
convex pseudo-envelops/ envelops $\alpha: (X, v) \to (\hat X, \hat v)$, 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 $\mathcal{QT}_d(Y, \mathbf c\Theta)$, the spaces $\mathcal
P_d^{\mathbf c\Theta}$ of real univariate polynomials of degree $d$ with real
divisors whose combinatorial types avoid the closed poset $\Theta$ play the
classical role of Grassmanians.
  We compute, in the homotopy-theoretical terms that involve $(\hat X, \hat v)$
and $\mathcal P_d^{\mathbf c\Theta}$, the quasitopies of convex envelops which
avoid the $\Theta$-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 $\mathcal{QT}_d(Y, \mathbf c\Theta)$ often
stabilize, as $d \to \infty$.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga