Reference : Invariance of the BFV complex
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/22555
Invariance of the BFV complex
English
Schatz, Florian mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2010
Pacific Journal of Mathematics
University of California
248
2
453-474
Yes (verified by ORBilu)
International
0030-8730
1945-5844
Berkeley
CA
[en] BFV-complex ; coisotropic submanifolds ; deformation theory
[en] The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold S of a Poisson manifold (M, \Pi).
However the assignment (coisotropic submanifold) -> (differential graded Poisson algebra) is not canonical, since in the construction several choices have to be made. One has to fix: 1. an embedding of the normal bundle NS of S into M as a tubular neighbourhood, 2. a connection on NS and 3. a special element Omega.
We show that different choices of a connection and an element Omega -- but
with the tubular neighbourhood fixed -- lead to isomorphic differential graded Poisson algebras. If the tubular neighbourhood is changed too, invariance can be restored at the level of germs.
Institute of Mathematics, University of Zurich (Zurich, Switzerland)
University of Zurich (Zurich, Switzerland) ; Swiss National Science Foundation (SNF-grant 200020-121640/1) ; European Union through the FP6 Marie Curie RTN ENIGMA (contract number MRTN-CT-2004-5652) ; European Science Foundation through the MISGAM program
Researchers
http://hdl.handle.net/10993/22555
10.2140/pjm.2010.248.453
http://msp.org/pjm/2010/248-2/p11.xhtml
The original publication is available at http://msp.org/pjm/2010/248-2/p11.xhtml

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