ﻻ يوجد ملخص باللغة العربية
For $Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurstons regularization theorem, first proved in cite{thurston}, without using Mathers homology equivalence. Moreover, in the co-orientable case, the resulting foliation can be chosen of a precise kind, namely an open book foliation modified by suspension. There is also a model in the non co-orientable case.
We prove the existence of a minimal (all leaves dense) foliation of codimension one, on every closed manifold of dimension at least 4 whose Euler characteristic is null, in every homotopy class of hyperplanes distributions, in every homotopy class of
A smooth fibration of $mathbb{R}^3$ by oriented lines is given by a smooth unit vector field $V$ on $mathbb{R}^3$, for which all of the integral curves are oriented lines. Such a fibration is called skew if no two fibers are parallel, and it is calle
In this paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact structures.
We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried
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 $partia