The Steenrod problem on realization of cycles: old and new

Singular homology groups form a basic invariant of a space, which allows to study its topological properties. Although they can be defined axiomatically, it is also useful (and quite agreeable) to think about them geometrically. In the late 1940s Steenrod asked whether a homology class can be represented by a continuous image of a fundamental class of a manifold. In the talk I will give an overview of results on this problem, presenting both classical and new ones.

The talk will be streamed through "Kontur Talk": https://mian.ktalk.ru/vhv429hulose?pinCode=9604