On smooth approximation of integral cycles mod 2
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914157013499904 |
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| author | Caldini, Gianmarco |
| author_facet | Caldini, Gianmarco |
| contents | We prove that every mod 2 integral cycle $T$ in a Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by a cycle which is a smooth submanifold $Σ$ of nearly the same area, up to a singular set of codimension 3; in addition, this estimate on the singular set can be refined depending on the codimension of the cycle. Moreover, if the mod 2 homology class $τ$ admits a smooth embedded representative, then $Σ$ can be chosen free of singularities. This article provides the unoriented version of the smooth approximation theorem for integral cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On smooth approximation of integral cycles mod 2 Caldini, Gianmarco Differential Geometry Analysis of PDEs We prove that every mod 2 integral cycle $T$ in a Riemannian manifold $\mathcal{M}$ can be approximated in flat norm by a cycle which is a smooth submanifold $Σ$ of nearly the same area, up to a singular set of codimension 3; in addition, this estimate on the singular set can be refined depending on the codimension of the cycle. Moreover, if the mod 2 homology class $τ$ admits a smooth embedded representative, then $Σ$ can be chosen free of singularities. This article provides the unoriented version of the smooth approximation theorem for integral cycles. |
| title | On smooth approximation of integral cycles mod 2 |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2511.10545 |