Immersed but not embedded homology classes

Abstract

We provide the first documented examples of immersions of closed oriented manifolds which are not homologous to embeddings, thus answering a question posed by Zhenhua Liu. In these examples we show that for any representing self-transverse immersion the double points must represent a non-trivial homology class in the source manifold. We also provide examples of Steenrod representable integral homology classes which are not represented by immersions.

We found a result of Massey and Peterson which proves Corollary 5.3 of v1, and hence Theorem 5.3 of v2. We then made corresponding minor changes to the Abstract, Introduction and Section 5. 15 pages