Dimensionsdefekt stetiger Abbildungen M⁴→S³

Abstract

In this note we shall prove the following statements: Let Mⁿ, n>3, be a compact, triangulated, n-dimensional mainfold with H²(Mⁿ)=0; let f: Mⁿ→S³ be an essential map onto the 3-sphere, Then there exist at most two points a and b, so that f⁻¹(a) and f⁻¹(b) are finite sets. If f: M⁴→S³ is essential, then there are at most two points a and b with dim f⁻¹(a)=0 and dim f⁻¹(b)=0.