Characteristic classes associated to Q-bundles

  title={Characteristic classes associated to Q-bundles},
  author={Alexei Kotov and Thomas Strobl},
  journal={International Journal of Geometric Methods in Modern Physics},
  • A. Kotov, T. Strobl
  • Published 26 November 2007
  • Mathematics
  • International Journal of Geometric Methods in Modern Physics
A Q-manifold is a graded manifold endowed with a vector field of degree 1 squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of "gauge fields" (sections in the category of graded manifolds) and each cohomology class of a certain subcomplex of forms on the fiber we associate a cohomology class on the base. As any principal bundle yields canonically a Q-bundle, this construction generalizes Chern–Weil classes… 

Dg Manifolds, Formal Exponential Maps and Homotopy Lie Algebras

This paper is devoted to the study of the relation between ‘formal exponential maps,’ the Atiyah class, and Kapranov L∞[1] algebras associated with dg manifolds in the C ∞ context. We prove that, for

The Atiyah class of a dg-vector bundle

Lie algebroid fibrations

The geometry of graded cotangent bundles

Local BRST cohomology for AKSZ field theories: a global approach I

We study the Lagrangian antifield BRST formalism, formulated in terms of exterior horizontal forms on the infinite order jet space of graded fields for topological field theories associated to

Connections adapted to non-negatively graded structures

  • A. Bruce
  • Mathematics
    International Journal of Geometric Methods in Modern Physics
  • 2019
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalization of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids, we

A higher Chern-Weil derivation of AKSZ sigma-models

Chern–Weil theory provides for each invariant polynomial on a Lie algebra 𝔤 a map from 𝔤-connections to differential cocycles whose volume holonomy is the corresponding Chern–Simons theory action

Graded Geometry, Q‐Manifolds, and Microformal Geometry

We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a



Q-algebroids and their cohomology

A Q-algebroid is a Lie superalgebroid equipped with a compatible homological vector field and is the infinitesimal object corresponding to a Q-groupoid. We associate to every Q-algebroid a double

On the structure of graded symplectic supermanifolds and Courant algebroids

This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles

BRST model for equivariant cohomology and representatives for the equivariant thom class

In this paper the BRST formalism for topological field theories is studied in a mathematical setting. The BRST operator is obtained as a member of a one parameter family of operators connecting the

The Geometry of the Master Equation and Topological Quantum Field Theory

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold,

Sur la suite exacte canonique associée à un fibré principal

Thé current algebra of a principle bundie is thé kernel of thé natural projection of thé Lie algebra of infinitésimal automorphisms of thé bundie onto thé Lie algebra of vector-fieids of ils base

Lie algebroids and homological vector fields

The notion of a Lie algebroid, introduced by J. Pradines, is an analogue of the algebra of a Lie group for differentiable groupoids. Lie algebroids combine the properties of Lie algebras and

Topological Open P-Branes

By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3-form C-field leads to deformations of the algebras of multi-vectors on the Dirichlet-brane world-volume as