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Journal of Lie Theory 29 (2019), No. 3, 629--646
Copyright Heldermann Verlag 2019

Homotopy Equivalence of Shifted Cotangent Bundles

Ricardo Campos
IMAG, University of Montpellier, 34090 Montpellier, France

Given a bundle of chain complexes, the algebra of functions on its shifted cotangent bundle has a natural structure of a shifted Poisson algebra. We show that if two such bundles are homotopy equivalent, the corresponding Poisson algebras are homotopy equivalent. We apply this result to L-algebroids to show that two homotopy equivalent bundles have the same L-algebroid structures and explore some consequences about the theory of shifted Poisson structures.

Keywords: Differential graded geometry, infinity algebroids, shifted Poisson structures.

MSC: 58A50, 18G55, 17B63

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