Rational homotopy theory is a simplified version of homotopy theory where the torsion on the homotopy groups of a space is discarded. It has the advantage of being remarkably computational and its simplicity makes it possible to address a number fundamental questions in topology and geometry. In this course we will present the Sullivan model for rational homotopy theory via commutative differential graded algebras and discuss some applications. In particular we will explain how to use the calculational force of rational homotopy theory to give answers to the closed geodesic problem: does every closed Riemannian manifold of dimension greater than one have infinitely many geometrically distinct closed geodesics?
Literature:
Yves Félix , Stephen Halperin , Jean-Claude Thomas, "Rational homotopy theory" (2001)
Dennis Sullivan, "Infinitesimal computations in topology" (1997)
Julian Holstein, "Rational homotopy theory", notes available online here
Bousfield and Gugenheim, "On PL De Rham theory and rational homotopy type" (1976)
Recommended previous knowledge:
Algebraic Topology I and II. Basic knowledge of singular cohomology and higher homotopy groups is recommended but not strictly necessary.
Time, Date and Location:
Monday 4-6 pm M102
Thursday 4-6 pm M102
Registration:
Registration for examination/ECTS: FlexNow
Additional comments:
There will be 4-5 exercises classes.
Course work:
Successful participation in the exercise classes
Examination:
Oral exam: duration 30 minutes, Date: tba, re-exam: Date: tba
Modules:
BV,MV, MarGeo, MGAGeo
ECTS:
6