On codimensions k immersions of m-manifolds for k = m - 3, k = m - 5 and k = m - 6

Abstract

Let us consider M be a closed smooth connected m-manifold, N be a smooth n-manifold and f: M → N be a continuousmapwith codimension k = n - m > 0. In this paper, under certain conditions, we prove that f is homotopic to an immersion, in the following cases: m ≡ (14) and codimension k = m - 3; m ≡ 2(4), m ≡ 3(8) and codimension k = m - 5; m ≡ 2(4), m ≡ 3(8) and codimension k = m - 6. This work complements some results of Biasi et al. [1, 2], Koschorke [9] and of Li and Li [5]. © 2010 Pushpa Publishing House.