147 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
Accidental parabolics and relatively hyperbolic groups
By constructing, in the relative case, objects analoguous to Rips and Sela's
canonical representatives, we prove that the set of images by morphisms without
accidental parabolic, of a finitely presented group in a relatively hyperbolic
group, is finite, up to conjugacy.Comment: Revision, 24 pages, 4 figure
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
A Combination Theorem for Metric Bundles
We define metric bundles/metric graph bundles which provide a purely
topological/coarse-geometric generalization of the notion of trees of metric
spaces a la Bestvina-Feighn in the special case that the inclusions of the edge
spaces into the vertex spaces are uniform coarsely surjective quasi-isometries.
We prove the existence of quasi-isometric sections in this generality. Then we
prove a combination theorem for metric (graph) bundles (including exact
sequences of groups) that establishes sufficient conditions, particularly
flaring, under which the metric bundles are hyperbolic. We use this to give
examples of surface bundles over hyperbolic disks, whose universal cover is
Gromov-hyperbolic. We also show that in typical situations, flaring is also a
necessary condition.Comment: v3: Major revision: 56 pages 5 figures. Many details added.
Characterization of convex cocompact subgroups of mapping class groups of
surfaces with punctures in terms of relative hyperbolicity given v4: Final
version incorporating referee comments: 63 pages 5 figures. To appear in
Geom. Funct. Ana
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
NKT sublineage specification and survival requires the ubiquitin-modifying enzyme TNF AIP3/A20
Natural killer T (NKT) cells are innate lymphocytes that differentiate into NKT1, NKT2, and NKT17 sublineages during development. However, the signaling events that control NKT sublineage specification and differentiation remain poorly understood. Here, we demonstrate that the ubiquitin-modifying enzyme TNF AIP3/A20, an upstream regulator of T cell receptor (TCR) signaling in T cells, is an essential cell-intrinsic regulator of NKT differentiation. A20 is differentially expressed during NKT cell development, regulates NKT cell maturation, and specifically controls the differentiation and survival of NKT1 and NKT2, but not NKT17, sublineages. Remaining A20-deficient NKT1 and NKT2 thymocytes are hyperactivated in vivo and secrete elevated levels of Th1 and Th2 cytokines after TCR ligation in vitro. Defective NKT development was restored by compound deficiency of MALT1, a key downstream component of TCR signaling in T cells. These findings therefore show that negative regulation of TCR signaling during NKT development controls the differentiation and survival of NKT1 and NKT2 cells
Selective C-Rel Activation via Malt1 Controls Anti-Fungal TH-17 Immunity by Dectin-1 and Dectin-2
C-type lectins dectin-1 and dectin-2 on dendritic cells elicit protective immunity against fungal infections through induction of TH1 and TH-17 cellular responses. Fungal recognition by dectin-1 on human dendritic cells engages the CARD9-Bcl10-Malt1 module to activate NF-κB. Here we demonstrate that Malt1 recruitment is pivotal to TH-17 immunity by selective activation of NF-κB subunit c-Rel, which induces expression of TH-17-polarizing cytokines IL-1β and IL-23p19. Malt1 inhibition abrogates c-Rel activation and TH-17 immunity to Candida species. We found that Malt1-mediated activation of c-Rel is similarly essential to induction of TH-17-polarizing cytokines by dectin-2. Whereas dectin-1 activates all NF-κB subunits, dectin-2 selectively activates c-Rel, signifying a specialized TH-17-enhancing function for dectin-2 in anti-fungal immunity by human dendritic cells. Thus, dectin-1 and dectin-2 control adaptive TH-17 immunity to fungi via Malt1-dependent activation of c-Rel
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