The homotopy type of shifted cotangent bundles

Description:  Given a vector bundle E over a smooth manifold M, the algebra of functions on its shifted cotangent bundle T*[1]E has a natural structure of a Lie algebra and solutions of the Maurer-Cartan equation correspond to Lie algebroid structures on E. Allowing E to be a dg bundle (bundle of chain complexes/ split Q-manifolds) we recover the notion of a Lie infinity algebroid. In this talk I will introduce the relevant objects, and explain how natural notions of homotopy equivalence of dg bundles give us equivalent Lie or Poisson algebras of functions and explore applications to infinity algebroids and to the theory of shifted Poisson structures. This work is based on arXiv:1803.07383v2 Date:  2019-07-12 Start Time:   14:30 Speaker:  Ricardo Campos (Univ. Montpellier, France) Institution:  CNRS - University of Montpellier Place:  Sala 5.5 Research Groups: -Geometry See more:   <Main>