122 research outputs found
Actions of arithmetic groups on homology spheres and acyclic homology manifolds
We establish lower bounds on the dimensions in which arithmetic groups with
torsion can act on acyclic manifolds and homology spheres. The bounds rely on
the existence of elementary p-groups in the groups concerned. In some cases,
including Sp(2n,Z), the bounds we obtain are sharp: if X is a generalized
Z/3-homology sphere of dimension less than 2n-1 or a Z/3-acyclic Z/3-homology
manifold of dimension less than 2n, and if n \geq 3, then any action of
Sp(2n,Z) by homeomorphisms on X is trivial; if n = 2, then every action of
Sp(2n,Z) on X factors through the abelianization of Sp(4,Z), which is Z/2.Comment: Final version, to appear in Math Zeitschrif
The symmetries of outer space
Published versio
Tree-irreducible automorphisms of free groups
We introduce a new class of automorphisms of the non-abelian free
group of finite rank which contains all iwips (= fully
irreducible automorphisms), but also any automorphism induced by a
pseudo-Anosov homeomorphism of a surface with arbitrary many boundary
components. More generally, there may be subgroups of of rank on
which restricts to the identity.
We prove some basic facts about such {\em tree-irreducible} automorphisms,
and show that, together with Dehn twist automorphisms, they are the natural
basic building blocks from which any automorphism of \FN can be constructed
in a train track set-up. We then show:
{\bf Theorem:} {\it Every tree-irreducible automorphism of has induced
North-South dynamics on the Thurston compactification of Outer
space.}
Finally, we define a "blow-up" construction on the vertices of a train track
map, which, starting from iwips, produces tree-irreducible automorphisms which
in general are not iwip
Dimension of the Torelli group for Out(F_n)
Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use
combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space
which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated
(n at least 3). In particular, this recovers the result of Krstic-McCool that
T_3 is not finitely presented. We also give a new proof of the fact, due to
Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure
Classical and quantum mechanical plane switching in CO2
Classical plane switching takes place in systems with a pronounced 1:2
resonance, where the degree of freedom with lowest frequency is
doubly-degenerate. Under appropriate conditions, one observes a periodic and
abrupt precession of the plane in which the doubly-degenerate motion takes
place. In this article, we show that quantum plane switching exists in CO2 :
Based on our analytical solutions of the classical Hamilton's equations of
motion, we describe the dependence on vibrational angular momentum and energy
of the frequency of switches and the plane switching angle. Using these
results, we find optimal initial wave packet conditions for CO2 and show,
through quantum mechanical propagation, that such a wave packet indeed displays
plane switching at energies around 10000 cm-1 above the ground state on time
scales of about 100 fs.Comment: accepted for publication in the Journal of Chemical Physic
Stability of the homology of the moduli spaces of Riemann surfaces with spin structure
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46234/1/208_2005_Article_BF01446896.pd
Intersection form, laminations and currents on free groups
Let be a free group of rank , let be a geodesic current
on and let be an -tree with a very small isometric action
of . We prove that the geometric intersection number is equal
to zero if and only if the support of is contained in the dual algebraic
lamination of . Applying this result, we obtain a generalization of
a theorem of Francaviglia regarding length spectrum compactness for currents
with full support. As another application, we define the notion of a
\emph{filling} element in and prove that filling elements are "nearly
generic" in . We also apply our results to the notion of \emph{bounded
translation equivalence} in free groups.Comment: revised version, to appear in GAF
Clinical and virological characteristics of hospitalised COVID-19 patients in a German tertiary care centre during the first wave of the SARS-CoV-2 pandemic: a prospective observational study
Purpose: Adequate patient allocation is pivotal for optimal resource management in strained healthcare systems, and requires detailed knowledge of clinical and virological disease trajectories. The purpose of this work was to identify risk factors associated with need for invasive mechanical ventilation (IMV), to analyse viral kinetics in patients with and without IMV and to provide a comprehensive description of clinical course.
Methods: A cohort of 168 hospitalised adult COVID-19 patients enrolled in a prospective observational study at a large European tertiary care centre was analysed.
Results: Forty-four per cent (71/161) of patients required invasive mechanical ventilation (IMV). Shorter duration of symptoms before admission (aOR 1.22 per day less, 95% CI 1.10-1.37, p < 0.01) and history of hypertension (aOR 5.55, 95% CI 2.00-16.82, p < 0.01) were associated with need for IMV. Patients on IMV had higher maximal concentrations, slower decline rates, and longer shedding of SARS-CoV-2 than non-IMV patients (33 days, IQR 26-46.75, vs 18 days, IQR 16-46.75, respectively, p < 0.01). Median duration of hospitalisation was 9 days (IQR 6-15.5) for non-IMV and 49.5 days (IQR 36.8-82.5) for IMV patients.
Conclusions: Our results indicate a short duration of symptoms before admission as a risk factor for severe disease that merits further investigation and different viral load kinetics in severely affected patients. Median duration of hospitalisation of IMV patients was longer than described for acute respiratory distress syndrome unrelated to COVID-19
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