Reference : BFV-complex and higher homotopy structures
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/22547
BFV-complex and higher homotopy structures
English
Schatz, Florian mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2009
Communications in Mathematical Physics
Springer Science & Business Media B.V.
286
2
399–443
Yes (verified by ORBilu)
International
0010-3616
1432-0916
[en] coisotropic submanifolds ; BFV-complex ; deformation theory
[en] We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are L-infinity quasi-isomorphic and control the same formal deformation problem.
However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instead.
Institute of Mathematics, University of Zurich (Zurich, Switzerland)
University of Zurich (Zurich, Switzerland) ; Swiss National Science Foundations (SNF-grant Nr.20-113439) ; European Union through the FP6 Marie Curie RTN ENIGMA (contract number MRTN-CT-2004- 5652) ; European Science Foundation through the MISGAM program ; Zurich Graduate School in Mathematics
Researchers
http://hdl.handle.net/10993/22547
10.1007/s00220-008-0705-0
http://link.springer.com/article/10.1007%2Fs00220-008-0705-0
The original publication is available at http://link.springer.com/article/10.1007%2Fs00220-008-0705-0

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
BFV-complex.pdfAuthor postprint500.09 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.