Immersed but not embedded homology classes
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913658410369024 |
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| author | Crowley, Diarmuid Grant, Mark |
| author_facet | Crowley, Diarmuid Grant, Mark |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Immersed but not embedded homology classes Crowley, Diarmuid Grant, Mark Geometric Topology 57R95, 57R42 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. |
| title | Immersed but not embedded homology classes |
| topic | Geometric Topology 57R95, 57R42 |
| url | https://arxiv.org/abs/2412.15359 |