2007/11/26 by Alexei Kotov, Kotov, Alexei, Thomas Strobl +1 · 3 citations
Mathematics · Physics and Astronomy · #55R10 #57R20 #58A50 #81T13 #81T45 #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.DG #math.MP #msc:55R10 #msc:57R20 #msc:58A50 #msc:81T13 #msc:81T45
paper · pdf · doi:10.48550/arxiv.0711.4106
23 pages, LaTeX, uses diagrams.sty
arxiv created 2007/11/26 · openalex publication_date 2007/11/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Q-manifold is a graded manifold endowed with a vector field of degree one 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. Any principal bundle yielding canonically a Q-bundle, this construction generalizes Chern-Weil classes. Novel examples include cohomology classes that are locally the de Rham differential of the integrands of topological sigma models obtained by the AKSZ-formalism in arbitrary dimensions. For Hamiltonian Poisson fibrations one obtains a characteristic 3-class in this manner. We also relate to equivariant cohomology and Lecomte's characteristic classes of exact sequences of Lie algebras.