Reference : Moduli of coisotropic Sections and the BFV-complex
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Moduli of coisotropic Sections and the BFV-complex
Schatz, Florian mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Asian Journal of Mathematics
International Press
71 - 100
[en] BFV-complex ; coisotropic submanifolds ; deformation theory
[en] We consider the local deformation problem of coisotropic submanifolds inside symplectic or Poisson manifolds. To this end the groupoid of coisotropic sections (with respect to some tubular neighbourhood) is introduced. Although the geometric content of this groupoid is evident, it is usually a very intricate object.
We provide a description of the groupoid of coisotropic sections in terms of a differential graded Poisson algebra, called the BFV-complex. This description is achieved by constructing a groupoid from the BFVcomplex and a surjective morphism from this groupoid to the groupoid of coisotropic sections. The kernel of this morphism can be easily chracterized.
As a corollary we obtain an isomorphism between the moduli space of coisotropic sections and the moduli space of geometric Maurer–Cartan elements of the BFV-complex. In turn, this also sheds new light on the geometric content of the BFV-complex.
Institute of Mathematics, University of Zurich (Zurich, Switzerland)
University of Zurich (Zurich, Switzerland) ; Swiss 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
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