Seminar Algebraic Topology: Rational Homotopy Theory
In Spring 2019 Lennart Meier and I are running a seminar for MSc students on rational homotopy theory. Here is the syllabus. We meet on Tuesdays, 1.15-3pm, in HFG610.
Some useful material for the seminar can be found here: Moerdijk's notes [Moe], Berglund's notes, and Hess' survey. A useful textbook reference is "Rational homotopy theory" by Félix, Halperin, and Thomas.
Feb 5, Gijs Heuts: Overview. Yuqing's notes.
Feb 12, Kevin Collins: Recollections on algebraic topology and the fibration theorem. Here are Kevin's notes, including the exercises to be handed in on Feb 19.
Feb 19, Pascal Sitbon: The rational Hurewicz and Whitehead theorems and rationalization of spaces. Pascal's notes, including the homework.
Feb 26, Jorge Becerra: Simplicial sets. Jorge's notes.
Mar 5, Jaco Ruit: Sullivan's polynomial differential forms and their basic properties. Jaco's notes.
Mar 12, Jack Davies: The de Rham complex and minimal models. Jack's notes.
Mar 19, Martijn Waal: More on minimal models and formal spaces.
Mar 26, Yuqing Shi: Relative Sullivan algebras and a minimal model for the fiber of a map. Yuqing's notes.
Apr 2: No seminar.
Apr 9, Jorge Becerra: Examples of minimal models and rational homotopy groups. Jorge's notes.
Apr 16, Kevin Collins: Minimal models of Lie groups, homogeneous spaces, and free loop spaces. Kevin's notes.
Apr 23, Jaco Ruit: Equivalence of homotopy theories between rational spaces and rational cdga's (with some hypotheses), I. Jaco's notes.
Apr 30, Martijn Waal: Equivalence of homotopy theories, II.
May 7, Pascal Sitbon: Formality of Kähler manifolds. Pascal's notes.
May 14, Yuqing Shi: Differential graded Lie algebras. Yuqing's notes.
May 21, Jack Davies. The rational dichotomy. Jack's notes.
May 28, Aldo Witte. Formality and symplectic manifolds. Aldo's notes.