


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 MaurerCartan equation correspond to Lie algebroid structures on E. Allowing E to be a dg bundle (bundle of chain complexes/ split Qmanifolds) 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: 
20190712

Start Time: 
14:30 
Speaker: 
Ricardo Campos (Univ. Montpellier, France)

Institution: 
CNRS  University of Montpellier

Place: 
Sala 5.5

Research Groups: 
Geometry

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