140 research outputs found

    Searching for Hyperbolicity

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    This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

    On the density of periodic configurations in strongly irreducible subshifts

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    Let GG be a residually finite group and let AA be a finite set. We prove that if XβŠ‚AGX \subset A^G is a strongly irreducible subshift of finite type containing a periodic configuration then periodic configurations are dense in XX. The density of periodic configurations implies in particular that every injective endomorphism of XX is surjective and that the group of automorphisms of XX is residually finite. We also introduce a class of subshifts XβŠ‚AZX \subset A^\Z, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense

    Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

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    This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic groups". We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called "Finding relative hyperbolic structures", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectivel

    Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

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    The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

    GATA3 Expression Is Decreased in Psoriasis and during Epidermal Regeneration; Induction by Narrow-Band UVB and IL-4

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    Psoriasis is characterized by hyperproliferation of keratinocytes and by infiltration of activated Th1 and Th17 cells in the (epi)dermis. By expression microarray, we previously found the GATA3 transcription factor significantly downregulated in lesional psoriatic skin. Since GATA3 serves as a key switch in both epidermal and T helper cell differentiation, we investigated its function in psoriasis. Because psoriatic skin inflammation shares many characteristics of epidermal regeneration during wound healing, we also studied GATA3 expression under such conditions

    Anosov representations: Domains of discontinuity and applications

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    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 Ξ“\Gamma into G we explicitly construct open subsets of compact G-spaces, on which Ξ“\Gamma 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
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