Related papers: Structured Topological Field Theories via Crossed …
Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal…
Under suitable hypotheses, we prove that a form of a projective homogeneous variety $G/P$ defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an algebro-geometric analogue of…
We construct a Frobenius algebra structure on the Hochschild cochains of a group ring k[G] that extends the known structure of a <1, 2> topological quantum field theory on HH^0(k[G]; k[G]), k a field and G a finite group. The convolution…
This note is to show the effectiveness of the notion of pseudoalgebra in the theory of conformal algebras. We adduce very simple construction of free associative conformal algebra and find its linear basis. There is no any new result but we…
We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their…
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…
We introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the…
This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction…
The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those…
Let $U$ be a smooth and connected curve over an algebraically closed field of positive characteristic, with smooth compactification $X$. We generalize classical Geometric Class Field theory to provide a classification of fppf $G$-torsors…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo $d$. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the…