Wednesday 24 January 2018, 16:00-17:00 in HG03.085
Gijs Heuts (Universiteit Utrecht)
Lie algebras and periodicity in homotopy theory
Quillen introduced the use of Lie algebras to study homotopy theory. He associated to every space X a differential graded Lie algebra over the rational numbers from which all rational invariants of X (e.g. rational cohomology and homotopy groups) can be calculated, thus translating the study of rational homotopy theory into algebra. The torsion in the homotopy groups of a space is generally harder to understand. It can be organized into certain periodic families and I will discuss how Lie algebras can be used to describe these as well.