We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.

We show that the deformation functor of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme admits miniversal pro-family, identifying its space first-order deformations with first hypercohomology complex which is naturally constructed out sheaf. also provide obstruction theory these objects whose target second this complex.

The cotangent bundle T X to a complex manifold X is classically endowed with the sheaf of k-algebras WT∗X of deformation quantization, where k := W{pt} is a subfield of C[[~, ~]. Here, we construct a new sheaf of k-algebras W TX which contains WT∗X as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra and prove that quantized symplectic transformations o...

In the framework of Abstract Differential Geometry, especially that dealing with vector sheaves (as expounded in [8]) and principal sheaves (initiated by [9]), we show that to a given principal sheaf (P ,G,X, π) together with a representation φ : G → GL(n,A), we associate a vector sheaf (E ,X, p). If φ is compatible with the representations of G and GL(n,A) into appropriate sheaves of Lie algeb...

We show that intersection homology extends Poincaré duality to manifold homotopically stratified spaces (satisfying mild restrictions). These spaces were introduced by Quinn to provide “a setting for the study of purely topological stratified phenomena, particularly group actions on manifolds.” The main proof techniques involve blending the global algebraic machinery of sheaf theory with local ...

We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algeb...