Topology Seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Applications of Rational Homotopy Theory
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, June 25
Venue: Room 215
Abstract: In my previous two talks, we discussed how Bousfield and Gugenheim reformulated Sullivan's rational homotopy theory within the framework of model categories and established a Quillen equivalence between suitable rational spaces and commutative differential graded algebras over Q.
In this talk, we begin with some applications of rational homotopy theory. First, we will see how rational homotopy theory provides a simple explanation for why the non-torsion part of the homotopy groups of spheres is concentrated in certain degrees, a result originally proved by Serre. We will then discuss another major application of rational homotopy theory, namely the solution of the closed geodesic problem due to Vigué-Poirrier and Sullivan, which relates the algebraic structure of the rational cohomology ring of a manifold to the existence of infinitely many closed geodesics.