Related papers: Vertical Genera
We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…
A noncommutative-geometric generalization of classical Weil theory of characteristic classes is presented, in the conceptual framework of quantum principal bundles. A particular care is given to the case when the bundle does not admit…
We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…
Given a vector bundle on a $\mathbb{P}^1$ bundle, the base is stratified by degeneracy loci measuring the spitting type of the vector bundle restricted to each fiber. The classes of these degeneracy loci in the Chow ring or cohomology ring…
We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation…
We study genus 2 covers of relative elliptic curves over an arbitrary base in which 2 is invertible. Particular emphasis lies on the case that the covering degree is 2. We show that the data in the "basic construction" of genus 2 covers of…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
We construct non-isogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.
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 construct the stable (representable) homotopy category of finite orbispectra, whose objects are formal desuspensions of finite orbi-CW-pairs by vector bundles and whose morphisms are stable homotopy classes of (representable) relative…
Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented cobordism ring N_*(X) of a topological space X. This homology theory Eh_* has coefficients Z/2 in every nonnegative…
We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…
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…
In this note we give a generalization for the higher order Hochschild cohomology and show that the secondary Hochschild cohomology is a particular case of this new construction.
For a more general notion of Cartan connection we define characteristic classes, we investigate their relation to usual characteristic classes.
The aim of the paper is to construct some Godbillon-Vey classes of a family of regular foliations, defined in the paper. These classes are cohomology classes on the manifold or on suitable open subsets. Some examples are also considered.
In this paper we construct various non-trivial and non-tautological cohomology classes on compactified and uncompactified strata of curves with a differential, by using the geometry of the boundary stratification of the moduli space of…
We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.
We show that the cobordism class of a polarization of Hodge module defines a natural transformation from the Grothendieck group of Hodge modules to the cobordism group of self-dual bounded complexes with real coefficients and constructible…