An intrinsically linked simplicial $n$-complex
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918159081013248 |
|---|---|
| author | Nikkuni, Ryo |
| author_facet | Nikkuni, Ryo |
| contents | For any positive integer $n$, Lovász-Schrijver, Taniyama and Skopenkov provided examples of simplicial $n$-complexes that inevitably contain a nonsplittable two-component link of $n$-spheres, no matter how they are embedded into the Euclidean $(2n+1)$-space. In this paper, we introduce a new example of such a simplicial $n$-complex through a simple argument in piecewise linear topology and an application of the van Kampen--Flores theorem. Furthermore, we demonstrate the existence of additional such complexes through higher dimensional generalizations of the $\triangle Y$-exchange on graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An intrinsically linked simplicial $n$-complex Nikkuni, Ryo Geometric Topology 57K45, 57M15 For any positive integer $n$, Lovász-Schrijver, Taniyama and Skopenkov provided examples of simplicial $n$-complexes that inevitably contain a nonsplittable two-component link of $n$-spheres, no matter how they are embedded into the Euclidean $(2n+1)$-space. In this paper, we introduce a new example of such a simplicial $n$-complex through a simple argument in piecewise linear topology and an application of the van Kampen--Flores theorem. Furthermore, we demonstrate the existence of additional such complexes through higher dimensional generalizations of the $\triangle Y$-exchange on graphs. |
| title | An intrinsically linked simplicial $n$-complex |
| topic | Geometric Topology 57K45, 57M15 |
| url | https://arxiv.org/abs/2509.19050 |