The transverse singular complex
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866910180730470400 |
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| author | Friedman, Greg Medina-Mardones, Anibal M. Sinha, Dev |
| author_facet | Friedman, Greg Medina-Mardones, Anibal M. Sinha, Dev |
| contents | Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial set $\mathrm{Sing}(M)$ of $M$ deformation retracts onto the simplicial subset $\mathrm{Sing}^{\mathcal{T}}\!(M)$ of smooth singular simplices that are transverse to every element of $\mathcal{T}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27984 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The transverse singular complex Friedman, Greg Medina-Mardones, Anibal M. Sinha, Dev Algebraic Topology Geometric Topology Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial set $\mathrm{Sing}(M)$ of $M$ deformation retracts onto the simplicial subset $\mathrm{Sing}^{\mathcal{T}}\!(M)$ of smooth singular simplices that are transverse to every element of $\mathcal{T}$. |
| title | The transverse singular complex |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2604.27984 |