For the Dirac operatorD on the standard quantum sphere we obtain an asymptotic expansion of the SUq(2)-equivariant entire cyclic cocycle corresponding to ε 1 2D when evaluated on the element k ∈ Uq(su2). The constant term of this expansion is a twisted cyclic cocycle which up to a scalar coincides with the volume form and computes the quantum as well as the classical Fredholm indices.

Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation t...

We define families of invariants for elements of the mapping class group of Σ, a compact orientable surface. Fix any characteristic subgroup H C π1(Σ) and restrict to J(H), any subgroup of mapping classes that induce the identity on π1(Σ)/H. To any unitary representation ψ of π1(Σ)/H is associated a higher-order ρψ-invariant and a signature 2-cocycle σψ . These signature cocycles are shown to b...

This paper presents a new construction of the m-fold metaplectic cover of GLn over an algebraic number field k, where k contains a primitive m-th root of unity. A 2-cocycle on GLn(A) representing this extension is given and the splitting of the cocycle on GLn(k) is found explicitly. The cocycle is smooth at almost all places of k. As a consequence, a formula for the Kubota symbol on SLn is obta...

We show that every measurable invariant conformal structure for a Hölder continuous linear cocycle over a subshift of finite type coincides almost everywhere with a continuous invariant conformal structure. We use this result to establish Hölder continuity of a measurable conjugacy between Hölder continuous cocycles where one of the cocycles is assumed to be uniformly quasiconformal. As a speci...

Let T be a measure-preserving and mixing action of a countable abelian group G on a probability space (X, S, μ) and A a locally compact second countable abelian group. A cocycle c : G × X 7−→ A for T disperses if limg→∞ c(g, ·) − α(g) = ∞ in measure for every map α : G −→ A. We prove that such a cocycle c does not disperse if and only if there exists a compact subgroup A0 ⊂ A such that the comp...

We study mixing properties of generalized T,T−1 transformations. discuss two mechanisms. In the case fiber dynamics is mixing, it sufficient that driving cocycle small with probability. only assumed to be ergodic, one needs use shearing cocycle. Applications include central limit theorem for sufficiently fast systems and estimates on deviations ergodic averages.

We investigate some issues regarding quantum corrections for de Sitter branes in a bulk AdS5 spacetime. The one-loop effective action for a Majorana spinor field is evaluated and compared with the scalar field result. We also evaluate the cocycle function for various boundary conditions, finding that the quantum corrections naturally induce higher order curvature terms in the original action an...

In this paper we investigate the cocycle actions of non-commutative Bernoulli shifts for a countable discrete group G on the AFD II1-factor N = ⊗g∈GMn(C) or ⊗g∈GR, where R is the AFD II1-factor. We show that if G contains some non-amenable exact group, then the fixed point algebra of any its cocycle action is always atomic. We also give another proof of Popa’s cocycle vanishing theorem [15] in ...

Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...