2025/2026
Геометрия и динамика гомеоморфизмов поверхностей
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Когда читается:
1, 2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Контактные часы:
60
Course Syllabus
Abstract
A self-homeomorphism of a surface is an object of TOPOLOGY. Considered up to homotopy, it gives rise to an element of the mapping class group, an important and powerful ALGEBRAIC invariant of a 2-manifold. It is determined by its action on a suitably chosen graph; hence it an object of COMBINATORICS. On the other hand, it can be iterated, and, for this reason, it is an object of DYNAMICAL SYSTEMS theory. Highly nontrivial and chaotic dynamics can arise from surface homeomorphisms. Finally, and most importantly, William Thurston in 1976 realized that a surface diffeomorphism endows a surface with an essentially unique GEOMETRY. This idea of Thurston has led to a classification of surface homeomorphisms that is satisfactory from both algebraic and dynamical viewpoints. Using the Nielsen-Thurston classification of surface homeomorphisms as a guiding line, we discuss relevant questions of surface topology, geometry, and dynamics.