Remarks on Immersions in the Metastable Dimension Range

Abstract

In this work we present a generalization of an exact sequence of normal bordism groups given in a paper by H. A. Salomonsen (Math. Scand. 32 (1973), 87-111). This is applied to prove that ifn < 2k, is a continuous map between two manifolds and g : M n → BO is the classifying map of the stable normal bundle of h such that (h, g) * :is an isomorphism for i < n − k and an epimorphism for i = n − k, then h bordant to an immersion implies that h is homotopic to an immersion. The second remark complements the result of C. Biasi, D. L. Gonçalves and A. K. M. Libardi (Topology Applic. 116 (2001), 293-303) and it concerns conditions for which there exist immersions in the metastable dimension range. Some applications and examples for the main results are also given.