Introduction to dg-manifolds, and homological vector fields - Part 3
We introduce the foundations of dg-manifolds, alias Q-manifolds, especially the Z-graded case, with a particular insistance on completion (we will use Kotov-Salnikov version of the latter). Although the material is well-known by experts, finding consistent references is not easy, so we hope that this mini-course fills a gap.
1 - Symmetric algebras, the problem of completion. Definition of Q-manifolds, their morphims and its homotopy equivalences. Boring and precise definitions. Red line will be : What makes sense geometrically in a Q-manifold?
2 - More insight about: what is the underlying geometry of a Q-manifold ? (Based on recent works by Kotov and Salnikov.)
3 - Exercices and examples.