Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

Streszczenie

Let $K$ be a $CW$-complex of dimension 3 such that $H^3(K;\mathbb Z)=0$, and $M$ a closed manifold of dimension~3 with a base point $a\in M$. We study the problem of existence of a map $f:K \to M$ which is strongly surjective, i.e. such that ${\rm MR} [f,a]\neq 0$. In particular if $M=S^1\times S^2$ we show that there is no $f:K \to S^1\times S^2$ which is strongly surjective. On the other hand, for $M$ the non-orientable $S^1$-bundle over $S^2$ there exists a complex $K$ and $f:K \to M$ such that ${\rm MR}[f,a]\neq 0$.