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2024/2025

Научно-исследовательский семинар "Локализация и рациональная теория гомотопий"

Статус: Дисциплина общефакультетского пула
Когда читается: 1, 2 модуль
Охват аудитории: для всех кампусов НИУ ВШЭ
Язык: английский
Кредиты: 6

Course Syllabus

Abstract

The homotopy category of CW-complexes is quite complicated. For example, given two simply-connected polyhedra, it is not clear how to tell whether they are homotopy equivalent, or to describe the homotopy classes of maps between them. It turns out however that these and other similar questions become much easier if we declare maps that induce isomorphisms of rational homology to be isomorphisms. The result is the {\it rational homotopy category}, in which the homotopy classes of maps and the homotopy equivalence classes of objects can be explicitly described.
Learning Objectives

Learning Objectives

  • -
Expected Learning Outcomes

Expected Learning Outcomes

  • ---
Course Contents

Course Contents

  • Eilenberg – MacLane spaces and Postnikov towers
  • Localising a space in a set of primes. Rationalisation.
  • Sullivan models of commutative differential graded algebras: existence and uniqueness
  • Examples of Sullivan models.
  • Applications of Sullivan models: homotopy groups; formality of Kähler manifolds; mapping class groups
  • Other models of rational homotopy types (𝐶∞-algebras, Lie models etc.)
  • Localisation of a category. Bousfield localisation
Assessment Elements

Assessment Elements

  • non-blocking Activity
  • non-blocking Home exam
Interim Assessment

Interim Assessment

  • 2024/2025 2nd module
    100% home exam.
Bibliography

Bibliography

Recommended Core Bibliography

  • Теория гомотопий, Ху Сы-Цзян, 1964

Recommended Additional Bibliography

  • Стабильные гомотопии и обобщенные гомологии, Адамс, Дж. Ф., 2013

Authors

  • GORINOV ALEKSEY GENNADEVICH
  • Иконописцева Юлия Вахтаногвна