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Rational Homotopy Theory

2020 – 2021, VIII, X semester

Course information

Topics:
Section 1: The problem of the rational theory of homotopy and the Sullivan functor.
1. Rational equivalence of spaces.
2. Commutative differential graded algebras.
3. Simplicial sets.
4. Rational differential forms.
5. The main theorem (statement)

Section 2: Formal spaces and minimal models.
1. Formal spaces.
2. H-spaces.
3. Kähler manifolds: basic information.
4. Formality of Kähler manifolds.
5. Minimum models.

Section 3: Technique of Sullivan’s Theory.
1. Homotopy in the category of algebras.
2. The geometric implementation of algebra.
3. Hirsch extensions and bundles
4. The rationalization of space.
5. Proof of the main theorem.
6. Features of a non-simply connected case.



Lecturers

Associate Professor