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On curves intersecting at most once.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Greene, Joshua Evan |
| Copyright Year | 2018 |
| Abstract | We prove that on a closed surface of genus $g$, the cardinality of a set of simple closed curves in which any two are non-homotopic and intersect at most once is $\lesssim g^2 \log(g)$. This bound matches the largest known constructions to within a logarithmic factor. The proof uses a probabilistic argument in graph theory. It generalizes as well to the case of curves that intersect at most $k$ times in pairs. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1807.05658v1.pdf |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1807.05658 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
