The Topology of the set of line Transversals
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916381963845632 |
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| author | Cheong, Otfried Goaoc, Xavier Holmsen, Andreas F. |
| author_facet | Cheong, Otfried Goaoc, Xavier Holmsen, Andreas F. |
| contents | We prove that for any set $F$ of $n\ge 2$ pairwise disjoint open convex sets in $\mathbb{R}^3$, the connected components of the set of lines intersecting every member of $F$ are contractible. The same result holds for directed lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14681 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Topology of the set of line Transversals Cheong, Otfried Goaoc, Xavier Holmsen, Andreas F. Metric Geometry We prove that for any set $F$ of $n\ge 2$ pairwise disjoint open convex sets in $\mathbb{R}^3$, the connected components of the set of lines intersecting every member of $F$ are contractible. The same result holds for directed lines. |
| title | The Topology of the set of line Transversals |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2205.14681 |