arXiv subjects

Alvaro del Pino

Publications and source records attributed to Alvaro del Pino.

3 recordsLinked to original sources

arXiv2016

Flexibility for tangent and transverse immersions in Engel manifolds

In this article we study immersions of the circle that are tangent to an Engel structure $\mathcal{D}$. We show that a full $h$-principle does exist as soon as one excludes the closed orbits of $\mathcal{W}$, the kernel of $\mathcal{D}$. This is sharp: we elaborate on work of Bryant and Hsu to show that curves tangent to $\mathcal{W}$ often conform additional isolated components that cannot be detected at a formal level. We then show that this is an exceptional phenomenon: if $\mathcal{D}$ is generic, curves tangent to $\mathcal{W}$ are not isolated anymore. We then go on to show that a full $h$-principle holds for immersions transverse to the Engel structure.

math.SG↗

arXiv2015

Foliated vector fields without periodic orbits

In this article parametric versions of Wilson's plug and Kuperberg's plug are discussed. We show that there is a weak homotopy equivalence induced by the inclusion between the space of non-singular vector fields tangent to a foliation and the subspace of those without closed orbits, as long as the leaves of the foliation have dimension at least 3. We contrast this with the case of foliations by surfaces in 3-manifolds.

math.DS↗

arXiv2014

H-principle for 4-dimensional contact foliations

In this article we introduce the topological study of codimension-1 foliations which admit contact or symplectic structures on the leaves. A parametric existence h-principle for foliated contact structures is provided for any cooriented foliation in a closed oriented 4-fold.

math.SG↗