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Topology 2. Lecture 3

2026LectureФёдор Вылегжанин

Singular homology — standard simplices and the inclusions of facets, singular simplices and chains, the differential; zeroth homology and path components, the homology of a point, reduced homology; chain maps and maps of homology, functoriality, the chain map induced by a continuous map; chain homotopies and the prism; the homotopy invariance theorem with a full proof via the prism operator; subcomplexes, quotient complexes and the homology of a pair.
1
550

Кластеризация и частичное обучение

2026LectureКонстантин Вячеславович Воронцов

Кластеризация и частичное обучение. Лекция курса «Машинное обучение» К. В. Воронцова. Постановка задачи кластеризации. Примеры прикладных задач. Типы кластерных структур.
0
260

Topology 2. Lecture 1

2026LectureФёдор Вылегжанин

Why homology is needed — the fundamental group as a functor, homotopy groups, bordism and its combinatorial approximation; chain complexes and their homology; abstract simplicial complexes, geometric realisation and triangulations; the complex of simplicial chains, the proof of d2=0d^2 = 0, the simplicial homology of a segment, of two points and of the boundary of a triangle; reduced homology.

1
470