Fedosov dg manifolds associated with Lie pairs

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Abstract

Given any pair (L, A) of Lie algebroids, we construct a differential graded manifold (L[1] ⊕ L/ A, Q) , which we call Fedosov dg manifold. We prove that the homological vector field Q constructed on L[1] ⊕ L/ A by the Fedosov iteration method arises as a byproduct of the Poincaré–Birkhoff–Witt map established in [18]. Finally, using the homological perturbation lemma, we establish a quasi-isomorphism of Dolgushev–Fedosov type: the differential graded algebras of functions on the dg manifolds (A[1] , dA) and (L[1] ⊕ L/ A, Q) are homotopy equivalent.

Original languageEnglish (US)
Pages (from-to)729-762
Number of pages34
JournalMathematische Annalen
Volume378
Issue number1-2
DOIs
StatePublished - Oct 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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