Related papers: Relative (generalized) differential cohomology

There are two natural candidates for the group of relative Cheeger-Simons differential characters. The first directly extends the work of Cheeger and Simons and the second extends the description given by Hopkins and Singer of the…

We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone…

We provide a suitable axiomatic framework for differential cohomology in the relative case and we deduce the corresponding long exact sequences. We also construct the relative version of the generalized Cheeger-Simons characters and we…

In the paper [1] (arXiv:math/0408333) the authors discuss two possible definitions of the relative Cheeger-Simons characters, the second one fitting into a long exact sequence. Here we relate that picture to the one of the relative Deligne…

In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded…

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…

We introduce relative homological and weakly homological categories, where ``relative'' refers to a distinguished class of normal epimorphisms. It is a generalization of homological categories, but also protomodular categories can be…

We explain how the approach of Andre and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.…

Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential…

We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this…

On the basis of Brylinski's work, we introduce a notion of equivariant smooth Deligne cohomology group, which is a generalization of both the ordinary smooth Deligne cohomology and the ordinary equivariant cohomology. Using the cohomology…

In this paper, we develop the theory of relative log convergent cohomology. We prove the coherence of relative log convergent cohomology in certain case by using the comparison theorem between relative log convergent cohomlogy and relative…

We construct a correspondence between the cohomology groups of a group $G$ relative to a family of subgroups $\famS$ and the classes of `relative extensions' of $G$ by abelian groups, modulo a certain equivalence relation. We establish this…

All the basic cohomology groups and reduced cohomology groups of the extended Schr\"odinger-Virasoro conformal algebra with trivial coefficients are completely determined. In particular, we introduce the notion of the relative cohomology of…

In Enochs' relative homological dimension theory occur the so called (co)resolvent and (co)proper dimensions which are defined using proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some…

We generalise to profinite groups some of our previous results on the cohomology of pro-p groups of bounded sectional p-rank.

Let h^{*} be a multiplicative cohomology theory, h_{*} its dual homology theory and \hat{h}^{*} a differential refinement. We first construct the natural pairing between h_{*} and the flat part of \hat{h}^{*}, generalizing the holonomy of a…

For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite…

Cheeger-Simons differential characters, Deligne cohomology in the smooth category, the Hopkins-Singer construction of ordinary differential cohomology and the recent Harvey-Lawson constructions are each in two distinct ways Abelian group…

We show that the cohomology groups usually associated with racks and quandles agree with the Quillen cohomology groups for the algebraic theories of racks and quandles, respectively. We also explain how this makes available the entire range…