On bordism groups of immersions

Abstract

The bordism group of immersions of oriented n n -manifolds into R n + k {{\mathbf {R}}^{n + k}} is identified with the stable homotopy group Π n + k s ( MSO ⁡ ( k ) ) \Pi _{n + k}^s(\operatorname {MSO} (k)) . We study these groups for n − 2 ⩽ k ⩽ n n - 2 \leqslant k \leqslant n , and discuss the behaviour of double points and their relation with the corresponding bordism groups of embeddings.