Degree One Maps and a Realization Theorem

Abstract

In [8] we classified degree one maps denned on Sp × Sg × Sr. In this paper we shall study degree one maps defined on the n-dimensional torus T = Sl × Sl × … × S1 as well as certain general properties of degree one maps. Theorem 1.1 must be known to experts; however we could not find it in the literature. Theorem 1.5 b) says that a Poincaré complex is nilpotent if it admits a degree one map from another nilpotent Poincaré complex. Theorem 1.5 a) means that certain stable properties are preserved by degree one maps and we use it later in Section 2.