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All stable characteristic classes of homological vector fields. (English) Zbl 1209.58006

Summary: An odd vector field \(Q\) on a supermanifold \(M\) is called homological if \(Q ^{2} = 0\). The Lie derivative \(L _{Q }\) makes the algebra of smooth tensor fields on \(M\) into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator \(L _{Q }\) and are represented by \(Q\)-invariant tensors made up of the homological vector field and a symmetric connection on \(M\) by means of algebraic tensor operations and covariant differentiation.

MSC:

58A50 Supermanifolds and graded manifolds
81T70 Quantization in field theory; cohomological methods
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
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