The homotopy type of the space of maps of a homology 3-sphere into the 2-sphere
Vagn Lundsgaard Hansen · Pacific Journal of Mathematics · 1978
It is proved that if K is a compact, connected polyhedron such that H 2 (K; Z) = 0, then all the components in the space of maps of K into the 2-sphere are homeomorphic.For K a polyhedral homology 3-sphere the common homotopy type of the components is identified and shown to be independent of K.