JournalsjncgVol. 16, No. 3pp. 927–966

The strong homotopy structure of Poisson reduction

  • Chiara Esposito

    Università degli Studi di Salerno, Fisciano, Italy
  • Andreas Kraft

    Polish Academy of Sciences, Warsaw, Poland
  • Jonas Schnitzer

    Albert-Ludwigs-Universität Freiburg, Germany
The strong homotopy structure of Poisson reduction cover
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Abstract

In this paper, we propose a reduction scheme for multivector fields phrased in terms of LL_\infty-morphisms. Using well-known geometric properties of the reduced manifolds, we perform a Taylor expansion of multivector fields, which allows us to build up a suitable deformation retract of differential graded Lie algebras (DGLAs). We first obtained an explicit formula for the LL_\infty-projection and -inclusion of generic DGLA retracts. We then applied this formula to the deformation retract that we constructed in the case of multivector fields on reduced manifolds. This allows us to obtain the desired reduction LL_\infty-morphism. Finally, we perform a comparison with other reduction procedures.

Cite this article

Chiara Esposito, Andreas Kraft, Jonas Schnitzer, The strong homotopy structure of Poisson reduction. J. Noncommut. Geom. 16 (2022), no. 3, pp. 927–966

DOI 10.4171/JNCG/455