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Rational Homotopy Theory SemesterSoSe 2023 Lecturer Luca Pol Type of course (Veranstaltungsart) Vorlesung German title Rationale Homotopietheorie Contents 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" Dennis Sullivan, "Infinitesimal computations in topology" 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 Monday 4-6 pm, Thursday 4-6 pm Location M102 Course homepage https://sites.google.com/view/lucapol/rational-homotopy-theory (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
There will be 4-5 exercises classes. Modules BV, MV, MArGeo, MGAGeo ECTS 6 |