Abstract
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.
| 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 |
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