BFV-complex; coisotropic submanifolds; deformation theory
Résumé :
[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.
Centre de recherche :
Institute of Mathematics, University of Zurich (Zurich, Switzerland)
Disciplines :
Mathématiques
Auteur, co-auteur :
SCHATZ, Florian ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Invariance of the BFV complex
Date de publication/diffusion :
2010
Titre du périodique :
Pacific Journal of Mathematics
ISSN :
0030-8730
eISSN :
1945-5844
Maison d'édition :
University of California, Berkeley, Etats-Unis - Californie
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
