373 research outputs found
Commutator length of annulus diffeomorphisms
We study the group of C^{r}-diffeomorphisms of the closed annulus that are
isotopic to the identity. We show that, for r different from 3, the linear
space of homogeneous quasi-morphisms on this group is one dimensional.
Therefore, the commutator length on this group is (stably) unbounded. In
particular, this provides an example of a manifold whose diffeomorphisms group
is unbounded in the sense of Burago, Ivanov and Polterovich
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
Link Invariants for Flows in Higher Dimensions
Linking numbers in higher dimensions and their generalization including gauge
fields are studied in the context of BF theories. The linking numbers
associated to -manifolds with smooth flows generated by divergence-free
p-vector fields, endowed with an invariant flow measure are computed in
different cases. They constitute invariants of smooth dynamical systems (for
non-singular flows) and generalizes previous results for the 3-dimensional
case. In particular, they generalizes to higher dimensions the Arnold's
asymptotic Hopf invariant for the three-dimensional case. This invariant is
generalized by a twisting with a non-abelian gauge connection. The computation
of the asymptotic Jones-Witten invariants for flows is naturally extended to
dimension n=2p+1. Finally we give a possible interpretation and implementation
of these issues in the context of string theory.Comment: 21+1 pages, LaTeX, no figure
The chameleon groups of Richard J. Thompson: automorphisms and dynamics
The automorphism groups of several of Thompson's countable groups of
piecewise linear homeomorphisms of the line and circle are computed and it is
shown that the outer automorphism groups of these groups are relatively small.
These results can be interpreted as stability results for certain structures of
PL functions on the circle. Machinery is developed to relate the structures on
the circle to corresponding structures on the line
On residualizing homomorphisms preserving quasiconvexity
H is called a G-subgroup of a hyperbolic group G if for any finite subset M G there exists a homomorphism from G onto a non-elementary hyperbolic group G_1 that is surjective on H and injective on M. In his paper in 1993 A. Ol'shanskii gave a description of all G-subgroups in any given non-elementary hyperbolic group G. Here we show that for the same class of G-subgroups the finiteness assumption on M (under certain natural conditions) can be replaced by an assumption of quasiconvexity
Upper bound on the density of Ruelle resonances for Anosov flows
Using a semiclassical approach we show that the spectrum of a smooth Anosov
vector field V on a compact manifold is discrete (in suitable anisotropic
Sobolev spaces) and then we provide an upper bound for the density of
eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real
axis and for large real parts.Comment: 57 page
Entropy of geometric structures
We give a notion of entropy for general gemetric structures, which
generalizes well-known notions of topological entropy of vector fields and
geometric entropy of foliations, and which can also be applied to singular
objects, e.g. singular foliations, singular distributions, and Poisson
structures. We show some basic properties for this entropy, including the
\emph{additivity property}, analogous to the additivity of Clausius--Boltzmann
entropy in physics. In the case of Poisson structures, entropy is a new
invariant of dynamical nature, which is related to the transverse structure of
the characteristic foliation by symplectic leaves.Comment: The results of this paper were announced in a talk last year in IMPA,
Rio (Poisson 2010
Hepatitis C viral evolution in genotype 1 treatment-naĂŻve and treatment-experienced patients receiving telaprevir-based therapy in clinical trials
Background: In patients with genotype 1 chronic hepatitis C infection, telaprevir (TVR) in combination with peginterferon and ribavirin (PR) significantly increased sustained virologic response (SVR) rates compared with PR alone. However, genotypic changes could be observed in TVR-treated patients who did not achieve an SVR.
Methods: Population sequence analysis of the NS3•4A region was performed in patients who did not achieve SVR with TVR-based treatment.
Results: Resistant variants were observed after treatment with a telaprevir-based regimen in 12% of treatment-naĂŻve patients (ADVANCE; T12PR arm), 6% of prior relapsers, 24% of prior partial responders, and 51% of prior null responder patients (REALIZE, T12PR48 arms). NS3 protease variants V36M, R155K, and V36M+R155K emerged frequently in patients with genotype 1a and V36A, T54A, and A156S/T in patients with genotype 1b. Lower-level resistance to telaprevir was conferred by V36A/M, T54A/S, R155K/T, and A156S variants; and higher-level resistance to telaprevir was conferred by A156T and V36M+R155K variants. Virologic failure during telaprevir treatment was more common in patients with genotype 1a and in prior PR nonresponder patients and was associated with higher-level telaprevir-resistant variants. Relapse was usually associated with wild-type or lower-level resistant variants. After treatment, viral populations were wild-type with a median time of 10 months for genotype 1a and 3 weeks for genotype 1b patients.
Conclusions: A consistent, subtype-dependent resistance profile was observed in patients who did not achieve an SVR with telaprevir-based treatment. The primary role of TVR is to inhibit wild-type virus and variants with lower-levels of resistance to telaprevir. The complementary role of PR is to clear any remaining telaprevir-resistant variants, especially higher-level telaprevir-resistant variants. Resistant variants are detectable in most patients who fail to achieve SVR, but their levels decline over time after treatment
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