All Stable Characteristic Classes of Homological Vector Fields

Details All Stable Characteristic Classes of Homological Vector Fields All Stable Characteristic Classes of Homological Vector Fields

2010-03-02

arxiv.org/abs/1003.0542v3

Lett.Math.Phys.94:243-261,2010

Physics

Mathematical Physics

17 pages, references and comments added

Scientific paper

10.1007/s11005-010-0434-0

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of 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 tensor operations.

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