2021/2022
Научно-исследовательский семинар "Введение в теорию кобордизмов"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Кредиты:
6
Контактные часы:
60
Course Syllabus
Abstract
The starting point of cobordism theory is the question whether or not one smooth manifold isthe boundary of another. This question and a few similar ones can be answered using homotopy theory. Viceversa, some of the strongest known results of homotopy theory make essential use of cobordisms of some typeor another.We will begin by looking at the Pontrjagin – Thom construction, which allows one to reduce the above questionand its variants (oriented, non-oriented, framed etc.) to calculating the homotopy groups of the corresponding Thom spectrum. Then we will study the classical applications. In particular, we will see that a smooth manifold bounds another smooth manifold if and only if all its Stiefel – Whitney numbers vanish. After that we will focuson complex cobordism and applications to homotopy theory.PREREQUISITES:Smooth manifolds as covered in the compulsory course; homology and cohomology ascovered in Algebraic topology 1 or the first three chapters of Hatcher’s Alegbraic topology.