285 citations · 738 across the 46 of their papers we have counts for
23 papers · 1 filter
The weighted projective superspace with weights and an analog of the Fubini--Study form
Ekaterina Shemyakova, Theodore Voronov
As a by-product of our work on super Plücker embedding, we came to the notion of a weighted projective superspace with weights . The construction is n…
On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms
Ekaterina Shemyakova, Theodore Voronov
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal -differential operators over a…
L-infinity bialgebroids and homotopy Poisson structures on supermanifolds
Theodore Voronov
We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold…
On super Plücker embedding and cluster algebras
Ekaterina Shemyakova, Theodore Voronov
We define a super analog of the classical Plücker embedding of the Grassmannian into a projective space. One of the difficulties of the problem is rooted in the fact that super ext…
Thick morphisms, higher Koszul brackets, and -algebroids
Hovhannes Khudaverdian, Theodore Voronov
It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowi…
Tangent functor on microformal morphisms, and non-linear pullbacks for forms and cohomology
Theodore Th. Voronov
We show how the tangent functor extends from ordinary smooth maps to "microformal morphisms" (also called "thick morphisms") of supermanifolds. Microformal morphisms generalize ord…
On volumes of classical supermanifolds
Theodore Voronov
We consider the volumes of classical supermanifolds such as the supersphere, complex projective superspace, and Stiefel and Grassmann supermanifolds, with respect to the natural me…
"Nonlinear pullbacks" of functions and -morphisms for homotopy Poisson structures
Theodore Th. Voronov
We introduce mappings between spaces of functions on (super)manifolds that generalize pullbacks with respect to smooth maps but are, in general, nonlinear (actually, formal). The c…
Geometry of differential operators of second order, the algebra of densities, and groupoids
H. M. Khudaverdian, Th. Th. Voronov
In our previous works, we introduced, for each (super)manifold, a commutative algebra of densities. It is endowed with a natural invariant scalar product. In this paper, we study g…
-manifolds and Higher Analogs of Lie Algebroids
Theodore Th. Voronov
We show how the relation between -manifolds and Lie algebroids extends to ``higher'' or ``non-linear'' analogs of Lie algebroids. We study the identities satisfied by a new alge…
On a non-Abelian Poincaré lemma
Theodore Voronov
We show that a well-known result on solutions of the Maurer--Cartan equation extends to arbitrary (inhomogeneous) odd forms: any such form with values in a Lie superalgebra satisfy…
Q-manifolds and Mackenzie theory: an overview
Theodore Voronov
This text is meant to be a brief overview of the topics announced in the title and is based on my talk in Vienna (August/September 2007). It does not contain new results (except pr…
Mackenzie theory and Q-manifolds
Theodore Th. Voronov
We give a simple characterization of Mackenzie's double Lie algebroids in terms of homological vector fields. Application to the `Drinfeld double' of Lie bialgebroids is given and…
Differential forms and odd symplectic geometry
Hovhannes M. Khudaverdian, Theodore Th. Voronov
We recall the main facts about the odd Laplacian acting on half-densities on an odd symplectic manifold and discuss a homological interpretation for it suggested recently by P. {Š}…
Geometry of differential operators, odd Laplacians, and homotopy algebras
Hovhannes Khudaverdian, Theodore Voronov
We give a complete description of differential operators generating a given bracket. In particular we consider the case of Jacobi-type identities for odd operators and brackets. Th…
Berezinians, Exterior Powers and Recurrent Sequences
H. M. Khudaverdian, Th. Th. Voronov
We study power expansions of the characteristic function of a linear operator in a -dimensional superspace . We show that traces of exterior powers of satisfy unive…
Geometry of differential operators, and odd Laplace operators
Hovhannes M. Khudaverdian, Theodore Voronov
We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar f…
On odd Laplace operators. II
Hovhannes M. Khudaverdian, Theodore Voronov
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive pict…
On odd Laplace operators
Hovhannes M. Khudaverdian, Theodore Voronov
We consider odd Laplace operators acting on densities of various weight on an odd Poisson (= Schouten) manifold . We prove that the case of densities of weight 1/2 (half-densiti…
On complexes related with calculus of variations
Hovhannes Khudaverdian, Theodore Voronov
We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The…
Graded manifolds and Drinfeld doubles for Lie bialgebroids
Theodore Voronov
We define \textit{graded manifolds} as a version of supermanifolds endowed with an additional -grading in the structure sheaf, called \textit{weight} (not linked with pa…
Dual Forms on Supermanifolds and Cartan Calculus
Theodore Voronov
The complex of "stable forms" on supermanifolds is studied. Stable forms on are represented by certain Lagrangians of "copaths" (formal systems of equations, which may or may n…
Quantization of Forms on Cotangent Bundle
Theodore Voronov
We consider the following construction of quantization. For a Riemannian manifold the space of forms on is made into a space of (full) symbols of operators acting on for…