Immersed but not embedded homology classes

Diarmuid Crowley; Mark Grant

doi:10.48550/arXiv.2412.15359

Immersed but not embedded homology classes

Diarmuid Crowley
, Mark Grant

Mathematical Science

University of Melbourne

Research output: Working paper › Preprint

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.

Original language	English
Publisher	ArXiv
Number of pages	15
DOIs	https://doi.org/10.48550/arXiv.2412.15359
Publication status	Published - 19 Dec 2024

Keywords

math.GT
57R95, 57R42

Access to Document

10.48550/arXiv.2412.15359Licence: Other

2412.15359v2Submitted manuscript, 232 KBLicence: Unspecified

Cite this

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Immersed but not embedded homology classes

Abstract

Keywords

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Cite this