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 |
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Keywords
- characteristic classes
- gauge theories
- Q-manifolds
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
All Stable Characteristic Classes of Homological Vector Fields. / Mosman, Elena; Sharapov, Alexey.
In: Letters in Mathematical Physics, Vol. 94, No. 3, 12.2010, p. 243-261.Research output: Contribution to journal › Article
}
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 -