On the immersion problem for certain manifolds

Abstract

In this note, let M denote a compact connected orientable C°°-manifold (with boundary) of dimension m, and R the A -dimensional Euclidean space. We write M^R (or MΦR) to denote the existence (or the non-existence) of a C°°-immersion of M into R. The purpose of this note is to discuss the immersion problem for some manifolds M whose integral cohomology groups H\M; Z) in positive dimensions are finite and have no 2-primary subgroups. We obtain the following immersion theorems of such manifolds M into R\ where h is near to 3m/2.