Related papers: Bar Complexes and Formality of Pull-backs

We consider a subclass of tilings, the tilings obtained by cut and projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponent \alpha in terms of the ranks of…

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…

Let $A$ be an abelian variety and $G$ a finite group of automorphisms of $A$ fixing the origin such that $A/G$ is smooth. The quotient $A/G$ can be seen as a fibration over an abelian variety whose fibers are isomorphic to a product of…

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for…

Let $\sigma\colon G \to S_n$ be a surjective homomorphism and let $H$ be a group. We introduce the \emph{permutational wreath pullback} \[ H \wr_\sigma G = H^n \rtimes_\sigma G, \] where the action of $G$ on $H^n$ is induced by permutation…

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…

We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a presentation of a module to an $R$-diagram. The latter is the…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…

In this short article we review how the classical theory of principal fibre bundles (PFB) transcribes in an algebraic formalism. In this dual formulation, a PFB is given by a right co-module algebra ${\cal P}$ over a Hopf algebra ${\cal H}$…

We show that hyperplane sections of strongly formal manifolds inherit strong formality. In particular, this property holds for generalized complete intersections defined by positive line bundles with trivial first de Rham cohomology group.…

We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of $V = F^{-1}(W)$ such that if $V$ has the property $A$, then $W$ must have the property $A$. We show that…

Motivated by recent results in graph C*-algebras concerning an equivariant pushout structure of the Vaksman-Soibelman quantum odd spheres, we introduce a class of graphs called trimmable. Then we show that the Leavitt path algebra of a…

Using Dolgushev's generalization of Fedosov's method for deformation quantization, we give a positive answer to a question of P.Xu: can one prove a formality theorem for Lie algebroids ? As a direct application of this result, we obtain…

Given a semistable fibration $f\colon X\to B$ we introduce a correspondence between foliations $\mathcal{F}$ on $X$ and local systems $\mathbb{L}$ on $B$. Building up on this correspondence we find conditions that give maximal rationally…

In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an…

We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…

We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.