Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of cross product C-algebras C0(X)⋊G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊G induced by the endomorphism, i.e. the Lefschetz numbe...

We give a complete list of all homogeneous spaces M = G/H where G is a simple compact Lie group, H a connected, closed subgroup, and G/H is simply connected, for which the isotropy representation of H on TpM decomposes into exactly two irreducible summands. For each homogeneous space, we determine whether it admits a G-invariant Einstein metric. When there is an intermediate subgroup H < K < G,...

Isotropy is a fundamental property of diffuse sound field. Although several studies have proposed an isotropy indicator to quantify the extent field, what not yet very clear how interpret quantified using these indicators. This study aims contribute understanding by (i) modifying existing based on spherical harmonic expansion and (ii) presenting isotropic field model composed finite number plan...

The circle group G is said to act pseudofreely if it is not free and if every orbit is one-dimensional and if the isotropy group is the identity except on isolated exceptional orbits where the isotropy group is the finite cyclic group Z(k), k > 1. We consider differentiable actions of this kind on homotopy seven spheres and classify all such actions. As a corollary, it follows that there can be...

Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product C-algebras C0(X)⋊ G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question expresses the graded trace of the map on rationalized K-theory of C0(X) ⋊ G induced by the endomorphism, i.e. the Lefschetz n...

The decay of large-scale anisotropies in small-scale turbulent flow is investigated. By introducing two different kinds of estimators we discuss the relation between the presence of a hierarchy for the isotropic and the anisotropic scaling exponents and the persistence of anisotropies. Direct measurements from a channel flow numerical simulation are presented. One of the main assumptions made b...

We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group G on TM and T ∗M based only on the knowledge of G and its action on M . Some applications to symplectic geometry are also shown.

A simple description of isotropy irreducible spaces G/K is given when G is a classical compact Lie group and K is compact and connected.

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian & Souradeep 2003 for CMB...