Novikov’s compact leaf theorem

2017 ◽  
pp. 87-101
Keyword(s):  
Compact Leaf

scholarly journals ON COLLINEAR CLOSED ONE-FORMS

2011 ◽  
Vol 84 (2) ◽  
pp. 322-336 ◽  
Author(s):  
IRINA GELBUKH
Keyword(s):  
Compact Leaf ◽  
Wedge Product ◽  
Singular Sets

AbstractWe study one-forms with zero wedge-product, which we call collinear, and their foliations. We characterise the set of forms that define a given foliation, with special attention to closed forms and forms with small singular sets. We apply the notion of collinearity to give a criterion for the existence of a compact leaf and to study homological properties of compact leaves.

Codimension-one foliations with one compact leaf

1989 ◽  
Vol 32 (3) ◽  
Author(s):  
Carlos Curr�s-Bosch
Keyword(s):  
Compact Leaf ◽  
Codimension One

scholarly journals Mapping quantitative trait loci and predicting candidate genes for leaf angle in maize

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245129
Author(s):  
Ning Zhang ◽  
Xueqing Huang
Keyword(s):  
Candidate Genes ◽  
Inbred Line ◽  
Plant Architecture ◽  
Crop Yields ◽  
Recombinant Inbred Lines ◽  
Chromosome 1 ◽  
Leaf Angle ◽  
Compact Leaf ◽  
Leaf Architecture ◽  
Maize Varieties

Leaf angle of maize is a fundamental determinant of plant architecture and an important trait influencing photosynthetic efficiency and crop yields. To broaden our understanding of the genetic mechanisms of leaf angle formation, we constructed a F3:4 recombinant inbred lines (RIL) population to map QTL for leaf angle. The RIL was derived from a cross between a model inbred line (B73) with expanded leaf architecture and an elite inbred line (Zheng58) with compact leaf architecture. A sum of eight QTL were detected on chromosome 1, 2, 3, 4 and 8. Single QTL explained 4.3 to 14.2% of the leaf angle variance. Additionally, some important QTL were confirmed through a heterogeneous inbred family (HIF) approach. Furthermore, twenty-four candidate genes for leaf angle were predicted through whole-genome re-sequencing and expression analysis in qLA02-01and qLA08-01 regions. These results will be helpful to elucidate the genetic mechanism of leaf angle formation in maize and benefit to clone the favorable allele for leaf angle. Besides, this will be helpful to develop the novel maize varieties with ideal plant architecture through marker-assisted selection.

Linéarisation symplectique en dimension 2

2001 ◽  
Vol 44 (2) ◽  
pp. 129-139
Author(s):  
Carlos Currás-Bosch
Keyword(s):  
Compact Leaf ◽  
Affine Structure ◽  
Transverse Coordinate ◽  
Lagrangian Foliation ◽  
Dimension 2

AbstractIn this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is , the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.

SURGERY AND FOLIATIONS OF KNOT COMPLEMENTS

1993 ◽  
Vol 02 (04) ◽  
pp. 369-397 ◽  
Author(s):  
JOHN CANTWELL ◽  
LAWRENCE CONLON
Keyword(s):  
Unit Ball ◽  
Lattice Points ◽  
Compact Leaf ◽  
Minimal Genus ◽  
Relative Homology ◽  
Topological Description ◽  
Seifert Surfaces ◽  
Knot Complements ◽  
Interesting Class

An interesting class of knots have complement with a remarkably simple topological description. This class includes all the arborescent knots with only even weights hence, in particular, the two bridge knots and many knots of ten or fewer crossings. For these knots, there are choices of minimal genus Seifert surfaces S such that all taut, depth one foliations of the knot complement, having S as sole compact leaf, can be classified up to isotopy. These foliations correspond exactly to the lattice points over the open faces of the unit ball in a Thurston-like norm on the relative homology of the complement of S.

MINIMALITY OF STRONG STABLE AND UNSTABLE FOLIATIONS FOR PARTIALLY HYPERBOLIC DIFFEOMORPHISMS

2002 ◽  
Vol 1 (4) ◽  
pp. 513-541 ◽  
Author(s):  
Christian Bonatti ◽  
Lorenzo J. Díaz ◽  
Raúl Ures
Keyword(s):  
Dense Subset ◽  
Subject Classification ◽  
Compact Leaf ◽  
Unstable Foliation ◽  
Stable Foliation ◽  
Hyperbolic Diffeomorphisms ◽  
Primary 37D25 ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Homoclinic Tangencies

We give a topological criterion for the minimality of the strong unstable (or stable) foliation of robustly transitive partially hyperbolic diffeomorphisms.As a consequence we prove that, for $3$-manifolds, there is an open and dense subset of robustly transitive diffeomorphisms (far from homoclinic tangencies) such that either the strong stable or the strong unstable foliation is robustly minimal.We also give a topological condition (existence of a central periodic compact leaf) guaranteeing (for an open and dense subset) the simultaneous minimality of the two strong foliations.AMS 2000 Mathematics subject classification: Primary 37D25; 37C70; 37C20; 37C29

scholarly journals Mapping quantitative trait loci and predicting candidate genes for leaf angle in maize

2020 ◽  
Author(s):  
Ning Zhang ◽  
Xueqing Huang
Keyword(s):  
Candidate Genes ◽  
Inbred Line ◽  
Plant Architecture ◽  
Crop Yields ◽  
Recombinant Inbred Lines ◽  
Chromosome 1 ◽  
Leaf Angle ◽  
Compact Leaf ◽  
Leaf Architecture ◽  
Maize Varieties

ABSTRACTLeaf angle of maize is a fundamental determinant of plant architecture and an important trait influencing photosynthetic efficiency and crop yields. To broaden our understanding of the genetic mechanisms of leaf angle formation, we constructed an F3:4 recombinant inbred lines (RIL) population derived from a cross between a model inbred line (B73) with expanded leaf architecture and an elite inbred line (Zheng58) with compact leaf architecture to map QTL for leaf angle. A sum of 8 QTL were detected on chromosome 1, 2, 3, 4 and 8. Single QTL explained 4.3 to 14.2% of the leaf angle variance. Additionally, some important QTL were confirmed through a heterogeneous inbred family(HIF) approach. Furthermore, twenty-four candidate genes for leaf angle were predicted through whole-genome resequencing and expression analysis in qLA02-01and qLA08-01 regions. These results will be helpful to elucidate the genetic mechanism of leaf angle formation in maize and benefit to clone the favorable allele for leaf angle or develop the novel maize varieties with ideal plant architecture through marker-assisted selection.

Structure of a foliated neighbourhood

1976 ◽  
Vol 79 (1) ◽  
pp. 101-110 ◽  
Author(s):  
Jenny Harrison
Keyword(s):  
Fibre Bundle ◽  
Extension Theorem ◽  
Holonomy Group ◽  
Structure Group ◽  
Compact Leaf ◽  
Discrete Structure ◽  
Covering Spaces

C. Ehresmann (2) has shown that if a leaf L of a smooth foliation has a foliated neighbourhood, then there exists a fibre bundle over L, normal to the leaves, with discrete structure group. Using the concept of a microbundle and the n-isotopy extension theorem, we find a similar result for both PL and TOP categories, and, in addition, show that the structure group can be chosen to be the holonomy group of L. As for applications we show that holonomy characterizes the foliated neighbourhood of a leaf (proved by Haefliger in the differentiable case (3)). In particular, if the holonomy group of a compact leaf L is trivial then the leaf has a trivial foliated neighbourhood, and if it is finite it has a neighbourhood of compact leaves which are covering spaces of L. Another corollary is the known result that a proper submersion with compact fibre is a fibration. Finally we use the fact that the constructed normal microbundle can be chosen to have its fibres contained in the leaves of a transverse foliation to demonstrate isotopy uniqueness of normal microbundles.

Sign in / Sign up

Export Citation Format

Share Document