Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Left orderability, foliations, and transverse $(\pi_1,\mathbb{R})$
  structures for $3$-manifolds with sphere boundary   Let $M$ be a closed orientable irreducible $3$-manifold with a left orderable
fundamental group, and $M_0 = M - Int(B^{3})$. We show that there exists a
Reebless co-orientable foliation $\mathcal{F}$ in $M_0$, whose leaves may be
transverse to $\partial M_0$ or tangent to $\partial M_0$ at their
intersections with $\partial M_0$, such that $\mathcal{F}$ has a transverse
$(\pi_1(M_0),\mathbb{R})$ structure, and $\mathcal{F}$ is analogue to taut
foliations (in closed $3$-manifolds) in the following sense: there exists a
compact $1$-manifold (i.e. a finite union of properly embedded arcs and/or
simple closed curves) transverse to $\mathcal{F}$ that intersects every leaf of
$\mathcal{F}$. We conjecture that $\mathcal{F}$ is obtained from removing a
$3$-ball foliated with horizontal disks from a taut foliation in $M$.

1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys