### Abstract

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 the algebraic tensor operations and covariant differentiation.

Original language | English |
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Pages (from-to) | 243-261 |

Number of pages | 19 |

Journal | Letters in Mathematical Physics |

Volume | 94 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 2010 |

Externally published | Yes |

### Keywords

- characteristic classes
- gauge theories
- Q-manifolds

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

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## Cite this

Mosman, E., & Sharapov, A. (2010). All Stable Characteristic Classes of Homological Vector Fields.

*Letters in Mathematical Physics*,*94*(3), 243-261. https://doi.org/10.1007/s11005-010-0434-0