Related papers: Kirillov structures up to homotopy
We prove a Hilbert-Samuel type result of arithmetic big line bundles in Arakelov geometry, which is an analogue of a classical theorem of Siu. An application of this result gives equidistribution of small points over algebraic dynamical…
By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…
We define \textit{graded manifolds} as a version of supermanifolds endowed with an additional $\mathbb Z$-grading in the structure sheaf, called \textit{weight} (not linked with parity). Examples are ordinary supermanifolds, vector bundles…
Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer-Cartan equations on corresponding governing differential graded Lie algebras using the big bracket construction of…
We show that any continuous $\mathbf{C}$-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator of order at most the rank of the bundle plus one.…
Construction of an infinite dimensional differentiable manifold ${\mathbb R}^{\infty}$ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra and a Weyl algebra bundle are presented.…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded…
A singular (or Hermann) foliation on a smooth manifold $M$ can be seen as a subsheaf of the sheaf $\mathfrak{X}$ of vector fields on $M$. We show that if this singular foliation admits a resolution (in the sense of sheaves) consisting of…
We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…
We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory 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…
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of…
Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed…
We generalize Demailly's construction of projective jet bundles and strictly negatively curved pseudometrics on them to the logarithmic case. We establish this logarithmic generalization explicitly via coordinates, just as Noguchi's…
Using the technique of higher derived brackets developed by Voronov, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic $2$-manifold. The algebra we obtain has a particularly nice structure,…
We give a homotopy theoretic characterization of stacks on a site $\cC$ as the {\it homotopy sheaves} of groupoids on $\cC$. We use this characterization to construct a model category in which stacks are the fibrant objects. We compare…
We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…
We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By ``simplicial algebra'' we mean any category of algebras over a simplicial algebraic theory,…
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and…