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BFV-Complex and Higher Homotopy Structures


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 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.

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Correspondence to Florian Schätz.

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Communicated by N. A. Nekrasov

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Schätz, F. BFV-Complex and Higher Homotopy Structures. Commun. Math. Phys. 286, 399 (2009).

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  • Vector Bundle
  • Poisson Algebra
  • Poisson Manifold
  • Grade Vector Space
  • Trivalent Vertex