Invariance of the BFV complex

Schatz, Florian

doi:10.2140/pjm.2010.248.453

Reference : Invariance of the BFV complex


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/22555

Title :	Invariance of the BFV complex
Language :	English
Author, co-author :	Schatz, Florian [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2010
Journal title :	Pacific Journal of Mathematics
Publisher :	University of California
Volume :	248
Issue/season :	2
Pages :	453-474
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0030-8730
e-ISSN :	1945-5844
City :	Berkeley
Country :	CA
Keywords :	[en] BFV-complex ; coisotropic submanifolds ; deformation theory
Abstract :	[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.
Research centres :	Institute of Mathematics, University of Zurich (Zurich, Switzerland)
Funders :	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
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/22555
DOI :	10.2140/pjm.2010.248.453
Other URL :	http://msp.org/pjm/2010/248-2/p11.xhtml
Mentions required by the publisher for OA :	The original publication is available at http://msp.org/pjm/2010/248-2/p11.xhtml

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