### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- characteristic classes
- gauge theories
- Q-manifolds

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Letters in Mathematical Physics*,

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

**All Stable Characteristic Classes of Homological Vector Fields.** / Mosman, Elena; Sharapov, Alexey.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 94, no. 3, pp. 243-261. https://doi.org/10.1007/s11005-010-0434-0

}

TY - JOUR

T1 - All Stable Characteristic Classes of Homological Vector Fields

AU - Mosman, Elena

AU - Sharapov, Alexey

PY - 2010/12

Y1 - 2010/12

N2 - An odd vector field Q on a supermanifold M is called homological, if Q2 = 0. The operator of Lie derivative LQ 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 LQ 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.

AB - An odd vector field Q on a supermanifold M is called homological, if Q2 = 0. The operator of Lie derivative LQ 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 LQ 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.

KW - characteristic classes

KW - gauge theories

KW - Q-manifolds

UR - http://www.scopus.com/inward/record.url?scp=78149498387&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149498387&partnerID=8YFLogxK

U2 - 10.1007/s11005-010-0434-0

DO - 10.1007/s11005-010-0434-0

M3 - Article

VL - 94

SP - 243

EP - 261

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 3

ER -