The Baum-Connes conjecture for hyperbolic groups

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups

Ideal bicombings for hyperbolic groups and applications

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established by Monod-Shalom hold for all non-elementary hyperbolic groups and their non-elementary subgroups. We also derive superrigidity results for actions of general irreducible lattices on a large class of hyperbolic metric spaces.Comment: Substantial generalizeation; now the results hold for a general class of hyperbolic metric spaces (rather than just hyperbolic groups

Combable groups have group cohomology of polynomial growth

Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees with the usual group cohomology and verify this condition for a class of combable groups. Our condition involves a chain complex that is closely related to exotic cohomology theories studied by Allcock and Gersten and by Mineyev.Comment: 19 pages, typo corrected in version

Flows and joins of metric spaces

We introduce the functor * which assigns to every metric space X its symmetric join *X. As a set, *X is a union of intervals connecting ordered pairs of points in X. Topologically, *X is a natural quotient of the usual join of X with itself. We define an Isom(X)-invariant metric d* on *X. Classical concepts known for H^n and negatively curved manifolds are defined in a precise way for any hyperbolic complex X, for example for a Cayley graph of a Gromov hyperbolic group. We define a double difference, a cross-ratio and horofunctions in the compactification X-bar= X union bdry X. They are continuous, Isom(X)-invariant, and satisfy sharp identities. We characterize the translation length of a hyperbolic isometry g in Isom(X). For any hyperbolic complex X, the symmetric join *X-bar of X-bar and the (generalized) metric d* on it are defined. The geodesic flow space F(X) arises as a part of *X-bar. (F(X),d*) is an analogue of (the total space of) the unit tangent bundle on a simply connected negatively curved manifold. This flow space is defined for any hyperbolic complex X and has sharp properties. We also give a construction of the asymmetric join X*Y of two metric spaces. These concepts are canonical, i.e. functorial in X, and involve no `quasi'-language. Applications and relation to the Borel conjecture and others are discussed.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper13.abs.htm

Director configuration of planar solitons in nematic liquid crystals

The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the general case of elastic anisotropy. The director field is continuous everywhere apart from a straight line segment whose length depends on the value of the magnetic field. This indicates the possibility of an elongated defect core for disclination lines in nematics due to an external magnetic field.Comment: 12 pages, Revtex, 8 postscript figure

Participation in the profile olympiads as estimation of effeciency of investments in education

В России обучающиеся школ активно участвуют в профильных олимпиадах, что позволяет школьникам проявить себя как личность, развивает интеллектуальные способности, а на прикладном уровне – высокие результаты дают возможность поступления в высшие учебные заведения. В статье проводится эмпирический анализ данных участия школьников в олимпиадах, который служит оценкой эффективности инвестиций в образование.There are many students of secondary educational organizations actively participate in profile Olympiads in Russia. Participation in olympiads allows schoolchildren to prove themselves as a person, develops intellectual abilities, and at the applied level – high results give the possibility of admission to higher educational institutions. The article provides an empirical analysis of data on participation in olympiads, which serves as an assessment of the effectiveness of investment in education

The cooperativity phenomena in a pigment-protein complex of light-harvesting antenna revealed by picosecond absorbance difference spectroscopy

AbstractA model of the cooperative changes in optical properties of light-harvesting bacteriochlorophyll molecules of complex B890 in response to the absorption of light quanta is proposed. According to the model, each antenna chromophore may persist in either of two optically non-excited states, R and T. The occurrence of at least one excitation per complex causes all optically non-excited chromophores of the complex to be converted from state R to state T. The theory is shown to be in good agreement with experimental ‘light curves’ (ΔAvs intensity of picosecond excitation pulse) for the ‘minor’ and ‘major’ signals of light-harvesting bacteriochlorophylls of complex B890 from Chromatium minutissimum