Property A and CAT(0) cube complexes

Property A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional CAT(0) cube complex the stabilisers of vertices at infinity are amenable

Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture

We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral algebraic K-theoretic (split) Novikov conjecture over \cpt and \S, where \cpt denotes the C^*-algebra of compact operators and \S denotes the algebra of Schatten class operators. We introduce assembly maps with finite coefficients and under an additional hypothesis, we prove that such a group also satisfies the algebraic K-theoretic Novikov conjecture over \bar{\mathbb{Q}} and \mathbb{C} with finite coefficients. For all torsion free Gromov hyperbolic groups G, we demonstrate that the canonical algebra homomorphism \cpt[G]\map C^*_r(G)\hat{\otimes}\cpt induces an isomorphism between their algebraic K-theory groups.Comment: v2 Exposition improved; one lemma and grant acknowledgement added; v3 some terminology changed and details added, Theorems 4.5 and 4.7 in v3 need an extra hypothesis; v4 abridged version accepted for publication in JHR

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Supramolecularly directed rotary motion in a photoresponsive receptor

Stimuli-controlled motion at the molecular level has fascinated chemists already for several decades. Taking inspiration from the myriad of dynamic and machine-like functions in nature, a number of strategies have been developed to control motion in purely synthetic systems. Unidirectional rotary motion, such as is observed in ATP synthase and other motor proteins, remains highly challenging to achieve. Current artificial molecular motor systems rely on intrinsic asymmetry or a specific sequence of chemical transformations. Here, we present an alternative design in which the rotation is directed by a chiral guest molecule, which is able to bind non-covalently to a light-responsive receptor. It is demonstrated that the rotary direction is governed by the guest chirality and hence, can be selected and changed at will. This feature offers unique control of directional rotation and will prove highly important in the further development of molecular machinery

The influence of keto defects on photoexcitation dynamics in polyfluorene

The optical properties of two differently substituted types of polyfluorenes, 9-monoalkylated PF (mono-PF) and 9,9-dialkylated PF (bi-PF) where studied by means of photo-induced absorption (PIA) and ultrafast pump and probe measurements. The photo-induced absorption was complemented by measurements on a fluorene-fluorenone copolymer, which can be seen as a model substance for the polyfluorenes containing keto-defect sites. By differential transmission measurements we show that for the 9-monoalkylated PF measurements the singlet and triplet signal is strongly reduced compared to the 9,9-dialkylated PF. Instead, the polaron signal becomes the dominant feature. © 2003 Elsevier B.V. All rights reserved