Immersed but not embedded homology classes

Diarmuid Crowley; Mark Grant

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arXiv · 2412.15359

Immersed but not embedded homology classes

Diarmuid Crowley·Mark Grant

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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.

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Diarmuid Crowley, Mark Grant. 2025-01-20. Immersed but not embedded homology classes. https://arxiv.org/abs/2412.15359

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