Oriented bordism groups of immersions

Abstract

Let IΩn, k denote the bordism group of immersions of closed oriented n-manifolds into (n + k)-space. The object of this paper is to study certain group extension problems arising from Pastor's calculations of IΩn, k.The bordism group of immersions was first studied by Wells [12] who calculated the unoriented bordism group I Rn, k for k = n and k = n − 1 ≡ 3(4). Later these unoriented bordism groups were completely determined by Koschorke and Olk for k ≥ n − 2 with the help of an exact sequence measuring the difference between IRn, k and Rn (see [4]). A similar program has been carried out by Pastor [7] to determine the oriented bordism group I Ωn, k for k ≥ n − 2 except for certain group extension problems and some low dimensional cases.