Immersed but not embedded homology classes

Fuente: arXiv
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Main Authors: Crowley, Diarmuid, Grant, Mark
Format: Preprint
Published: 2024
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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