Reference : BFV-complex and higher homotopy structures
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
BFV-complex and higher homotopy structures
Schatz, Florian mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Communications in Mathematical Physics
Springer Science & Business Media B.V.
Yes (verified by ORBilu)
[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
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