Related papers: A Class of Topological Actions
We propose a general notion of parallel transport on $\sf RCD$ spaces, prove an unconditioned uniqueness result and existence under suitable assumptions on the space.
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
We give a mathematical formalization of `generalized data parallel' operations, a concept that covers such common scientific kernels as matrix-vector multiplication, multi-grid coarsening, load distribution, and many more. We show that from…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
The theory of coalgebras, for an endofunctor on a category, has been proposed as a general theory of transition systems. We investigate and relate four generalizations of bisimulation to this setting, providing conditions under which the…
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
Assuming complex functions defined on complex curves satisfy recursion relations with respect to number of parameters, we express the corresponding cohomology theory via generalizations of holomorphic connections. In examples provided, the…
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…
We give a survey of cyclic homology/cohomology theory including a detailed discussion of cyclic theories for various classes of topological algebras. We show how to associate cyclic classes with Fredholm modules and $K$-theory classes and…
It is known that the Picard group of a complex manifold can be expressed as a Deligne cohomology group. One may wonder if the same holds for the Picard group of a smooth algebraic variety and Deligne-Beilinson cohomology but this is not…
A unified theoretical description of ballistic and diffusive carrier transport in parallel-plane semiconductor structures is developed within the semiclassical model. The approach is based on the introduction of a thermo-ballistic current…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We recall the cohomological interpretation of the unipotent quotients of the fundamental groupoid of an algebraic complex variety (Beilinson, Deligne-Goncharov). We then give a construction of the resutting transition morphisms in terms of…
This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne…
Multiple types can represent the same concept. For example, lists and trees can both represent sets. Unfortunately, this easily leads to incomplete libraries: some set-operations may only be available on lists, others only on trees.…
We consider intersecting hypersurfaces in curved spacetime with gravity governed by a class of actions which are topological invariants in lower dimensionality. Along with the Chern-Simons boundary terms there is a sequence of intersection…
New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improved versions of the expressions written in [V. M. Zhdanov. Transport Processes in Multicomponent…
The motivation for this paper stems \cite{CR} from the need to construct explicit isomorphisms of (possibly nontrivial) principal $G$-bundles on the space of loops or, more generally, of paths in some manifold $M$, over which I consider a…