Symplectic groups are N-determined 2-compact groups

We show that for n>=3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus

Smooth actions of connected compact Lie groups with a free point are determined by two vector fields

Consider a smooth action $\mathbf G\times M \rightarrow M$ of a compact connected Lie group $\mathbf G$ on a connected manifold $M$. Assume the existence of a point of $M$ whose isotropy group has a single element (free point). Then we prove that there exist two complete vector field $X,X_1$ such that their group of automorphisms equals $\mathbf G$ regarded as a group of diffeomorphisms of $M$ (the existence of a free point implies that the action of $\mathbf G$ is effective). Moreover, some examples of effective actions with no free point where this result fails are exhibited.Comment: 30 pages, no figures. V2: Major revision. Exposition improved and added a new section presenting some open question

Soil Organic Carbon and Total Nitrogen in a \u3ci\u3eLeucaena leucocephala\u3c/i\u3e Silvopastoral System in the Chaco Region, Argentina

The introduction of leucaena (Leucaena leucocephala) into hedgerow silvopastoral systems increases animal production and improves soil fertility, through biological nitrogen fixation and deep-rooted leguminous trees. There is limited information on carbon and nitrogen dynamics in hedgerow silvopastoral systems, particularly in long term periods and subsoil profiles. The concentrations and vertical distribution of organic carbon (OC) and total nitrogen (TN), and their fractions (particulate and associate forms) in the soil profile (0‒100 cm), with and without leucaena were compared 10 years after leucaena establishment into a 24-year-old tropical pasture (Urochloa brizantha-Chloris gayana). Leucaena increased the OC concentration in the deepest horizon (50‒100 cm) by 73% (from 0.40 to 0.69%), particularly the stable form (associate OC). This was attributed to a greater abundance of leucaena roots deeper in the profile than in the pure grass pasture. Leucaena also enhanced by 12% the TN concentration in the topsoil (0‒20 cm) (from 0.133 to 0.149%) and by 21% in deepest horizon (from 0.049 to 0.059%) associated with leaf deposition, recycling of animal feces and nodule-N turnover from N fixation. Although TN increased in the leucaena topsoil and it is expected that OC follows the same pattern, OC concentration decreased in the topsoil. The low OC content in the topsoil of the leucaena pasture was closely linked to the poor grass cover observed (r2 = 0.82). The loss in grass cover was attributed to the excessive grazing pressure imposed to control the height of leucaena hedgerows. Leucaena establishment has the potential to improve soil fertility and hence availability of N to companion grass growth, and can be utilized as a greenhouse gas mitigation strategy. However, to achieve the potential productivity and carbon sequestration of leucaena in silvopastoral systems, grass persistence needs to be evaluated under different management practices and grazing regimes

Groups as automorphisms of dessins d'enfants

It is known that every finite group can be represented as the full group of automorphisms of a suitable compact dessin d'enfant. In this paper, we give a constructive and easy proof that the same holds for any countable group by considering non-compact dessins. Moreover, we show that any tame action of a countable group is so realizable