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.
By Camille Laurent-Gengoux
By Camille Laurent-Gengoux
By Camille Laurent-Gengoux
By Benoît Fresse
By Benoît Fresse
By Benoît Fresse
By Benoît Fresse
By Benoît Fresse
By Benoît Fresse
By Olivier Schiffmann
By Olivier Schiffmann
By Olivier Schiffmann
By Olivier Schiffmann
By Olivier Schiffmann
By Adrian Ocneanu
By Vladimir Salnikov
By Serguei Merkulov
By Bernhard Keller
By Bernhard Keller
By Ronnie Pavlov
By Tamara Kucherenko
