A crucial property of the standard antifield-BRST cohomology at non negative ghost number is that any cohomological class is completely determined by its antifield independent part. In particular, a BRST cocycle that vanishes when the antifields are set equal to zero is necessarily exact. This property, which follows from the standard theorems of homological perturbation theory, holds not only ...

We show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant. Further we show that it completely determines invertibility and positive/negative amphicheirality of hyperbolic knots.

A new characterisation of planar graphs is presented. It concerns the structure of the cocycle space of a graph, and is motivated by consideration of the dual of an elementary property enjoyed by sets of circuits in any graph.

We study the exponential dichotomy of an exponentially bounded, strongly continuous cocycle over a continuous ow on a locally compact metric space acting on a Banach space X. Our main tool is the associated evolution semigroup on C 0 ((; X). We prove that the cocycle has exponential dichotomy if and only if the evolution semi-group is hyperbolic if and only if the imaginary axis is contained in...

We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras H and those for cocycle twists H of H. This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups ur,s(sln) under conditions on the parameters guaranteeing th...

The cocycle super-rigidity theorem is a central result in the study of dynamics of semisimple Lie groups and lattices. We give an overview of the main ideas centered on this theorem and some of its most immediate applications. The emphasis will be on the topological and differentiable (as opposed to measurable) aspects of the theory.

We compute the algebraic hull of the Kontsevich– Zorich cocycle over any GL2 (R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.

Assuming that the underlying probability space is non-atomic we prove that products of random matrices (linear cocycles) with simple Lyapunov spectrum form an L p-dense set (1 p < 1) in the space of all cocy-cles satisfying the integrability conditions of the multiplicative ergodic theorem. However, the linear cocycles with one-point spectrum are also L p-dense. Further, in any L 1-neighborhood...

In this paper we study systematically the Euclidean renormalization in configuration spaces. We investigate also the deviation from commutativity of the renormalization and the action of all linear partial differential operators. This deviation is the source of the anomalies in quantum field theory, including the renormalization group action. It also determines a Hochschild 1–cocycle and the re...

In this note we show the spectral mapping theorem for the evolution semigroup on L p ((; ; X), 1 p < 1, associated with a strongly continuous cocycle on a Banach space over a continuous ow on a locally compact metric space.