Related papers: Infinitesimal index: cohomology computations
A numerical index is introduced for semigroups of completely positive maps of $\Cal B(H)$ which generalizes the index of E_0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its…
We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.
We formulate and prove a version of the Segal Conjecture for infinite groups. For finite groups it reduces to the original version. The condition that G is finite is replaced in our setting by the assumption that there exists a finite model…
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear supergroup. Some of these classes restrict to the universal…
We motivate and survey the theory of BPS invariants of categories and BPS cohomology of stacks, indicating applications in enumerative geometry and representation theory, as well as recent advances.
In this work we obtain the general form of polynomial mappings that commute with a linear action of a relative symmetry group. The aim is to give results for relative equivariant polynomials that correspond to the results for relative…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
Finding the number of maximal subgroups of infinite index of a finitely generated group is a natural problem that has been solved for several classes of `geometric' groups (linear groups, hyperbolic groups, mapping class groups, etc). Here…
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The…
Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of…
For the tensor of coherences parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at infinitesimal level. The main advantage of this formalism (clearly reminiscent of the…
We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…
This submission is a PhD dissertation. It constitutes the summary of the author's work concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. It includes the…
We study the invariant distributions for the horocycle map on $\Gamma\backslash SL(2, \mathbb{R})$ and prove Sobolev estimates for the cohomological equation of the horocycle map. As an application, we obtain an estimate for the rate of…
We use sheaf theory and the six operations to define and study the (equivariant) homology of stacks. The construction makes sense in the algebraic, complex-analytic, or even topological categories.
We define a local intersection number for metrised line bundles over quasiprojective varieties with compact support and show the local arithmetic Hodge index theorem for this intersection number. As a consequence we obtain a uniqueness…
Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…
Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.