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arXiv · 1803.07383

Homotopy equivalence of shifted cotangent bundles

Ricardo Campos
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Abstract

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 $L_\infty$-algebroids to show that two homotopy equivalent bundles have the same $L_\infty$-algebroid structures and explore some consequence on the theory of shifted Poisson structures.

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Ricardo Campos. 2018-03-20. Homotopy equivalence of shifted cotangent bundles. https://arxiv.org/abs/1803.07383

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