
Journal of Lie Theory 29 (2019), No. 3, 629646 Copyright Heldermann Verlag 2019 Homotopy Equivalence of Shifted Cotangent Bundles Ricardo Campos IMAG, University of Montpellier, 34090 Montpellier, France ricardo.campos@umontpellier.fr 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 [ Fulltextpdf (240 KB)] for subscribers only. 