Journal of Lie Theory

no. 3
Homotopy Equivalence of Shifted Cotangent Bundles
Journal of Lie Theory, Volume 29 (2019) no. 3, pp. 629-646
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.
DOI: 10.5802/jolt.1074
Classification: 58A50, 18G55, 17B63
Keywords: Differential graded geometry, infinity algebroids, shifted Poisson structures 
@article{JOLT_2019_29_3_a3,
     author = {R. Campos},
     title = {Homotopy {Equivalence} of {Shifted} {Cotangent} {Bundles}},
     journal = {Journal of Lie Theory},
     pages = {629--646},
     year = {2019},
     volume = {29},
     number = {3},
     doi = {10.5802/jolt.1074},
     zbl = {1442.58003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1074/}
}
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%J Journal of Lie Theory
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R. Campos. Homotopy Equivalence of Shifted Cotangent Bundles. Journal of Lie Theory, Volume 29 (2019) no. 3, pp. 629-646. doi: 10.5802/jolt.1074

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