2024/2025
Research Seminar "Localisation and Rational Homotopy Theory"
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Open to:
students of all HSE University campuses
Instructors:
Alexei Gorinov
Language:
English
ECTS credits:
6
Contact hours:
60
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.