Related papers: Cohomologie non abelienne d'ordre superieur et app…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…

Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups $\mathrm{SCG}$ are…

The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…

We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental…

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 give a Orlik-Solomon type presentation for the cohomology ring of arrangements in a non-compact abelian Lie group. The new insight consists in comparing arrangements in different abelian groups. Our work is based on the Varchenko-Gelfand…

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.

In this note we show that the theory of non abelian extensions of a Lie algebra $\mathfrak{g}$ by a Lie algebra $\mathfrak{h}$ can be understood in terms of a differential graded Lie algebra $L$. More precisely we show that the non-abelian…

In this paper we define a notion of gerbed tower, and use this notion to give a geometric representation of cohomological classes.

We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain…

We propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermathematics. We also prove generalizations of a number of…

A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…

We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this…

Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper, we show how the context of a `noetherian form', recently…

In this paper we introduce and study the basic properties of de Rham cohomology for a certain class of non-Hausdorff manifolds. After a careful discussion of non-Hausdorff differential forms, we provide a description of de Rham cohomology…

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

In this note, the notion of cotorsion classes is introduced into the higher homological algebra. Our results motivate the definition, showing that this notion of $n$-cotorsion classes satisfies usual properties one could expect. In…

Higher homological algebra, basically done in the framework of an $n$-cluster tilting subcategory $\mathcal{M}$ of an abelian category $\mathcal{A}$, has been the topic of several recent researches. In this paper, we study a relative…

We give an overview of differential cohomology from a modern, homotopy-theoretic perspective in terms of sheaves on manifolds. Although modern techniques are used, we base our discussion in the classical precursors to this modern approach,…