Let F be a smooth foliation on a closed Riemannian manifold M , and let Λ be a transverse invariant measure of F . Suppose that Λ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then a topological definition of the Λ-Lefschetz number of any leaf preserving diffeomorphism (M,F) → (M,F) is given. For this purpose, standard results about smooth approximation a...

We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus T, n ≥ 2, namely codimension one foliations, flows, and the so-called nonquadratic foliations. We show in particular that non-quadratic foliations are rigid, in the sense that they do not admit transverse diffeomorphisms other than ±id and translations. The computation is an app...

Some years ago we introduced a new topological invariant for foliated manifolds using techniques from noncommutative geometry, in particular the pairing between K-Theory and cyclic cohomology. The motivation came from flat principal G-bundles where the base space is a non simply connected manifold. The computation of this invariant is quite complicated. In this article we try to perform certain...

We classify the Fibonacci chains (F-chains) by their index sequences and construct an approximately finite dimensional (AF) C-algebra on the space of F-chains as Connes did on the space of Penrose tiling. The K-theory on this AF-algebra suggests a connection between the noncommutative torus and the space of F-chains. A noncommutative torus, which can be regarded as the C-algebra of a foliation ...

BACKGROUND AND AIMS There is a growing concern about how forests will respond to increased herbivory associated with climate change. Carbon (C) and nitrogen (N) limitation are hypothesized to cause decreasing growth after defoliation, and eventually mortality. This study examines the effects of a natural and massive defoliation by an insect on mature trees' C and N storage, which have rarely be...

Folding of the cortex and the persistence of radial glia (RG)-like cells called Bergmann glia (BG) are hallmarks of the mammalian cerebellum. Similar to basal RG in the embryonic neocortex, BG maintain only basal processes and continuously express neural stem cell markers. Past studies had focused on the function of BG in granule cell migration and how granule cell progenitors (GCP) regulate ce...

Geophysical and rheological work below the subduction seismogenic zone suggest that elevated pore fluid pressures (Pfs) may facilitate slow slip tremor. However, quantification of Pf its variation in this environment remain indirect incomplete. We examine brittle-frictional deformation within metasedimentary rocks from an exhumed zone. Here, penetrative foliation formed under viscous conditions...

Let ω be a differential q-form defining foliation of codimension q in projective variety. In this article we study the singular locus various settings. We relate certain type singularities, which name persistent, with unfoldings ω, generalizing previous work done on foliations 1 space. also absence persistent singularities existence connection sheaf 1-forms foliation.