We will discuss the classical N. Steenrod’s problem on realization of (integral singular) homology classes by continuous images of smooth manifolds. Apart from discussing classical results, I will present some of my own. Namely: the construction in each degree n of homology class x such that the minimal multiplicity with which it is realizable in the above sense is equal to the maximal odd divisor of [(n-1)/2]! and proving that in all dimensions less or equal to 23 this estimate is exact.
The talk will be in Russian.