817 research outputs found
The definability criterions for convex projective polyhedral reflection groups
Following Vinberg, we find the criterions for a subgroup generated by
reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index
subgroups to be definable over where is an integrally
closed Noetherian ring in the field . We apply the criterions for
groups generated by reflections that act cocompactly on irreducible properly
convex open subdomains of the -dimensional projective sphere. This gives a
method for constructing injective group homomorphisms from such Coxeter groups
to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of
\SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In
particular, we consider simplicial reflection groups that are isomorphic to
hyperbolic simplicial groups and classify all the conjugacy classes of the
reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over
. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure
On compatibility between isogenies and polarisations of abelian varieties
We discuss the notion of polarised isogenies of abelian varieties, that is,
isogenies which are compatible with given principal polarisations. This is
motivated by problems of unlikely intersections in Shimura varieties. Our aim
is to show that certain questions about polarised isogenies can be reduced to
questions about unpolarised isogenies or vice versa.
Our main theorem concerns abelian varieties B which are isogenous to a fixed
abelian variety A. It establishes the existence of a polarised isogeny A to B
whose degree is polynomially bounded in n, if there exist both an unpolarised
isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As
a further result, we prove that given any two principally polarised abelian
varieties related by an unpolarised isogeny, there exists a polarised isogeny
between their fourth powers.
The proofs of both theorems involve calculations in the endomorphism algebras
of the abelian varieties, using the Albert classification of these endomorphism
algebras and the classification of Hermitian forms over division algebras
Compact pseudo-Riemannian manifolds with parallel Weyl tensor
It is shown that in every dimension n=3j+2, j=1,2,3,..., there exist compact
pseudo-Riemannian manifolds with parallel Weyl tensor, which are
Ricci-recurrent, but neither conformally flat nor locally symmetric, and
represent all indefinite metric signatures. The manifolds in question are
diffeomorphic to nontrivial torus bundles over the circle. They all arise from
a construction that a priori yields bundles over the circle, having as the
fibre either a torus, or a 2-step nilmanifold with a complete flat torsionfree
connection; our argument only realizes the torus case.Comment: 19 page
Anosov representations: Domains of discontinuity and applications
The notion of Anosov representations has been introduced by Labourie in his
study of the Hitchin component for SL(n,R). Subsequently, Anosov
representations have been studied mainly for surface groups, in particular in
the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this
article we extend the notion of Anosov representations to representations of
arbitrary word hyperbolic groups and start the systematic study of their
geometric properties. In particular, given an Anosov representation of
into G we explicitly construct open subsets of compact G-spaces, on which
acts properly discontinuously and with compact quotient.
As a consequence we show that higher Teichmueller spaces parametrize locally
homogeneous geometric structures on compact manifolds. We also obtain
applications regarding (non-standard) compact Clifford-Klein forms and
compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica
Lack of Foxp3 function and expression in the thymic epithelium
Foxp3 is essential for the commitment of differentiating thymocytes to the regulatory CD4+ T (T reg) cell lineage. In humans and mice with a genetic Foxp3 deficiency, absence of this critical T reg cell population was suggested to be responsible for the severe autoimmune lesions. Recently, it has been proposed that in addition to T reg cells, Foxp3 is also expressed in thymic epithelial cells where it is involved in regulation of early thymocyte differentiation and is required to prevent autoimmunity. Here, we used genetic tools to demonstrate that the thymic epithelium does not express Foxp3. Furthermore, we formally showed that genetic abatement of Foxp3 in the hematopoietic compartment, i.e. in T cells, is both necessary and sufficient to induce the autoimmune lesions associated with Foxp3 loss. In contrast, deletion of a conditional Foxp3 allele in thymic epithelial cells did not result in detectable changes in thymocyte differentiation or pathology. Therefore, in mice the only known role for Foxp3 remains promotion of T reg cell differentiation within the T cell lineage, whereas there is no role for Foxp3 in thymic epithelial cells
The XXL Survey VII: A supercluster of galaxies at z=0.43
The XXL Survey is the largest homogeneous and contiguous survey carried out
with XMM-Newton. Covering an area of 50 square degrees distributed over two
fields, it primarily investigates the large-scale structures of the Universe
using the distribution of galaxy clusters and active galactic nuclei as tracers
of the matter distribution. Given its depth and sky coverage, XXL is
particularly suited to systematically unveiling the clustering of X-ray
clusters and to identifying superstructures in a homogeneous X-ray sample down
to the typical mass scale of a local massive cluster. A friends-of-friends
algorithm in three-dimensional physical space was run to identify large-scale
structures. In this paper we report the discovery of the highest redshift
supercluster of galaxies found in the XXL Survey. We describe the X-ray
properties of the clusters members of the structure and the optical follow-up.
The newly discovered supercluster is composed of six clusters of galaxies at a
median redshift z around 0.43 and distributed across approximately 30 by 15 arc
minutes (10 by 5 Mpc on sky) on the sky. This structure is very compact with
all the clusters residing in one XMM pointing; for this reason this is the
first supercluster discovered with the XXL Survey. Spectroscopic follow-up with
WHT (William Herschel Telescope) and NTT (New Technology Telescope) confirmed a
median redshift of z = 0.43. An estimate of the X-ray mass and luminosity of
this supercluster and of its total gas mass put XLSSC-e at the average mass
range of superclusters; its appearance, with two members of equal size, is
quite unusual with respect to other superclusters and provides a unique view of
the formation process of a massive structure.Comment: A&A, accepted; special XXL issu
Flux Confinement in Mesoscopic Superconductors
We report on flux confinement effects in superconducting submicron line, loop
and dot structures. The main idea of our study was to vary the boundary
conditions for confinement of the superconducting condensate by taking samples
of different topology and, through that, modifying the lowest Landau level
E_{LLL}(H). Since the critical temperature versus applied magnetic field
T_{c}(H) is, in fact, E_{LLL}(H) measured in temperature units, it is varied as
well when the sample topology is changed. We demonstrate that in all studied
submicron structures the shape of the T_{c}(H) phase boundary is determined by
the confinement topology in a unique way.Comment: 10 pages, 5 EPS figures, uses LaTeX's sup.sty, contribution to a
special issue of "Superlattices and Microstructures
Semitoric integrable systems on symplectic 4-manifolds
Let M be a symplectic 4-manifold. A semitoric integrable system on M is a
pair of real-valued smooth functions J, H on M for which J generates a
Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall
introduce new global symplectic invariants for these systems; some of these
invariants encode topological or geometric aspects, while others encode
analytical information about the singularities and how they stand with respect
to the system. Our goal is to prove that a semitoric system is completely
determined by the invariants we introduce
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