Related papers: Local cohomology -- an invitation
In this paper we describe the homology and cohomology of some natural bimodules over the little discs operad, whose components are configurations of non-$k$-overlapping discs. At the end we briefly explain how this algebraic structure…
In this paper, we present an overview of the development of one of the most dynamic areas of mathematics today: local differential operators of non-integer order. The underlying question is whether we are witnessing a period of…
The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
We point out a simple characterisation of topological amenability in terms of bounded cohomology, following Johnson's reformulation of amenability.
This talk gives a brief introduction to black hole horizons and their role in black hole thermodynamics. In particular a distinction is made between quasi-locally defined horizons and event horizons. Currently some new techniques have led…
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…
Let $R$ be a polynomial ring over a field. We introduce the concept of sequentially almost Cohen-Macaulay modules and describe the extremal rays of the cone of local cohomology tables of finitely generated graded $R$-modules which are…
In this survey, we give an introduction to nearly K\"ahler geometry, and list some results on submanifolds of these spaces. This survey tries by no means to be complete.
We characterize quasihomogeneity of isolated singularities by the injectivity of the map induced by the first differential of the logarithmic differential complex in the top local cohomology supported in the singular point.
We survey decades of research identifying the (co)homology of configuration spaces with Lie algebra (co)homology. The different routes to this one proto-theorem offer genuinely different explanations of its truth, and we attempt to convey…
Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.
We construct a framework which gives intuitive representation of local cohomology groups. By defining the concrete mappings among them, we show their equivalence. As an application, we justify intuitive representation of Laplace…
In this note we prove an equivariant version of a result of Cartan for equivariant simplicial cohomology with local coefficients.
Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the integral cohomology of the locally symmetric space Gamma\D. The…
This paper is a very brief introduction to idempotent mathematics and related topics.
This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.
This thesis is comprised of three chapters. The first chapter deals with bounded complexes of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative homological algebra, we approximate such complexes with…
The paper is devoted to the study of mappings with non--bounded characteristics of quasiconformality. The analog of the theorem about radius injectivity of locally quasiconformal mappings was proved for some class of mappings. There are…
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.