140 research outputs found
Searching for Hyperbolicity
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
Let be a residually finite group and let be a finite set. We prove
that if is a strongly irreducible subshift of finite type
containing a periodic configuration then periodic configurations are dense in
. The density of periodic configurations implies in particular that every
injective endomorphism of is surjective and that the group of automorphisms
of is residually finite. We also introduce a class of subshifts , 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
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
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
Non-Canonical NF-ΞΊB Activation and Abnormal B Cell Accumulation in Mice Expressing Ubiquitin Protein Ligase-Inactive c-IAP2
Loss of c-IAP2 ubiquitin ligase activity, which occurs in the lymphoma-causing c-IAP2/MALT1 fusion protein, activates non-canonical NF-ΞΊB signaling and results in B cell abnormalities characteristic of MALT lymphoma
GATA3 Expression Is Decreased in Psoriasis and during Epidermal Regeneration; Induction by Narrow-Band UVB and IL-4
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
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
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