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Butterflies I: Morphisms of 2-group stacks
Abstract Weak morphisms of non-abelian complexes of length 2, or crossed modules, are morphisms of the associated 2-group stacks, or gr-stacks. We present a full description of the weak morphisms inExpand
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Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces
Abstract:We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus g > 1, and present a rigorous invariantExpand
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2-Gerbes bound by complexes of gr-stacks, and cohomology
Abstract We define 2-gerbes bound by complexes of braided group-like stacks. We prove a classification result in terms of hypercohomology groups with values in abelian crossed squares and cones ofExpand
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Free field representation of Toda field theories
We study the following problem: Can a classical sln Toda field theory be represented by means of free bosonic oscillators through a Drinfeld-Sokolov construction? We answer affirmatively in the caseExpand
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Toda field theory as a clue to the geometry of Wn-gravity
We discuss geometrical aspects of Toda Fields generalizing the links between Liouville gravity and uniformization of Riemann surfaces of genus greater than one. The framework is the interplay betweenExpand
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Cup products, the Heisenberg group, and codimension two algebraic cycles
We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety.Expand
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The lagrangian approach to stochastic variational principles on curved manifolds
The classical definition of the action functional, for a dynamical system on curved manifolds, can be extended to the case of diffusion processes. For the stochastic action functional so obtained, weExpand
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Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings
We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional trivialityExpand
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Le bilan jeunes rejoignants, un outil d'évaluation des acquis et des potentiels
Cet outil de bilan est destine a evaluer les acquis et les potentiels des jeunes, francophones ou non, qui arrivent en France suite a une procedure de regroupement familial. Il permet de recenser lesExpand
Stacks of Ann-Categories and their morphisms
We show that $\mathit{ann}$-categories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. MoreExpand
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