Algebra Seminar 

22/05/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Thomas Kahl, Universidade do Minho, Braga

Introduction to Rational Homotopy Theory

The purpose of this talk is to provide an introduction to the main techniques and results of rational homotopy theory. No original results will be presented.

To any simply connected space one can associate two algebraic objects - its Quillen model, which is a differential graded Lie algebra, and its Sullivan model, which is a commutative differential graded algebra. The algebraic models of a space contain all its rational homotopy information and have been used by Y. Félix and S. Halperin to establish a dichotomy in rational homotopy theory: Any simply connected finite CW-complex $X$ is either elliptic, i.e., $\dim {\pi }_{*}(X)\otimes Q<\infty$, or hyperbolic, i.e., the sequence $\dim {\pi }_{\le n}(X)\otimes Q$ grows exponentially.