All Stable Characteristic Classes of Homological Vector Fields

Abstract

An odd vector field Q on a supermanifold M is called homological, if Q² = 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	https://doi.org/10.1007/s11005-010-0434-0
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

Access to Document

10.1007/s11005-010-0434-0

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author = "Elena Mosman and Alexey Sharapov",

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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.

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KW - Q-manifolds

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