Promoting Essential Laminations

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuine laminations. In the second case, M satisfies the weak geometrization conjecture - either its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is atoroidal, the mapping class group of M is finite, and any automorphism homotopic to the identity is isotopic to the identity.Comment: 56 pages, 11 figures; version 3: final version, incorporates referee's suggestion

3-Manifolds Everywhere

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in the few relators model, and the density model of random groups (at any density less than a half).Danny Calegari was supported by NSF grant DMS 1005246. Henry Wilton was supported by an EPSRC Career Acceleration Fellowship

A highly conserved circular RNA is required to keep neural cells in a progenitor state in the mammalian brain

circSLC45A4 is the main RNA splice isoform produced from its genetic locus and one of the highest expressed circRNAs in the developing human frontal cortex. Knockdown of this highly conserved circRNA in a human neuroblastoma cell line is sufficient to induce spontaneous neuronal differentiation, measurable by increased expression of neuronal marker genes. Depletion of circSlc45a4 in the developing mouse cortex causes a significant reduction of the basal progenitor pool and increases the expression of neurogenic regulators. Furthermore, knockdown of circSlc45a4a induces a significant depletion of cells in the cortical plate. In addition, deconvolution of the bulk RNA-seq data with the help of single-cell RNA-seq data validates the depletion of basal progenitors and reveals an increase in Cajal-Retzius cells. In summary, we present a detailed study of a highly conserved circular RNA that is necessary to maintain the pool of neural progenitors in vitro and in vivo

On bi-invariant word metrics

We prove that bi-invariant word metrics are bounded on certain Chevalley groups. As an application we provide restrictions on Hamiltonian actions of such groups.Comment: 16 pages; few typos from printed version correcte

Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

Soil physical properties affected by soil management and crop rotation in a long term experiment in Southern Brazil

The main objective of this work is to evaluate soil physical properties affected by cover crop rotations and soil management after 19 years of applying NoTill and Conventional Tillage systems with different winter species on a clayey Oxisol in South Brazil

Long-term effect of different soil management systems and winter crops on soil acidity and vertical distribution of nutrients in a Brazilian Oxisol

“Strategies” to sustain crop productivity by reducing the fertilizer and lime demands must be developed. The use of plant species that use more efficiently the soil nutrients and tillage systems that provide nutrients accumulation in more labile forms are prerequisites for sustainable agroecosystems. This study aimed to evaluate the long period effect of cultivating different winter species under different soil management systems on vertical distribution of soil nutrients and the soil acidity distribution in soil profile. The experiment was established in 1986 with six winter treatments (blue lupine, hairy vetch, oat, radish, wheat and fallow) under conventional tillage (CT) and no-tillage (NT) in a very clayey Rhodic Hapludox in Southern Brazil. As a result of 19 years of no soil disturbance, soil chemical attributes related to soil acidity and the availability of P and K were more favorable to crops growth up to 10 cm in the soil under no-tillage than in the conventional tillage. On other hand, lime applications in low doses on the soil surface were not efficient in neutralizing the aluminum toxicity below 10 cm depth. It shows that repeated use of lime on the soil surface under NT system can be a viable alternative strategy only when soil acidity and aluminum toxicity in subsurface has been previously eliminated using the adequate amount of lime and incorporating it into the arable layer. Moreover, in the conventional tillage system P and K availability were higher below 10 cm depth compared to the no-tillage system. Even after 19 years of no soil disturbance in the NT system the available P content below 10 cm soil layer was lower than the optimal content of available P recommended to cash crops. The reduced surface K application over time was sufficient to gain adequate crop yields and to maintain the optimal content of soil available K in both soil management systems. The effects of soil management systems were predominant on the soil acidity attributes, and no effects of winter cover crops were observed on soil acidity attributes. Black oat and blue lupine were more efficient in P cycling, increasing the soil available P content especially in the surface soil under NT. The lower amount of biomass produced over time when no cover crops were used in the winter period resulted in lower P and K availability in the soil, showing the important role of growing winter species to maintain soil fertility