Authors: | Blagojević, Pavle Dimitrijević-Blagojević, Aleksandra McCleary, John |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Equilateral triangles on a Jordan curve and a generalization of a theorem of Dold | Journal: | Topology and its Applications | Volume: | 156 | Issue: | 1 | First page: | 16 | Last page: | 23 | Issue Date: | 1-Nov-2008 | Rank: | M23 | ISSN: | 0166-8641 | DOI: | 10.1016/j.topol.2008.04.008 | Abstract: | Let γ : S1 → R2 be a Jordan curve in the plane. It is a simple topological riddle to determine if there is an equilateral triangle with vertices on γ. By reformulating this question in the paradigm of configuration spaces and test maps, we can solve this riddle using a Borsuk-Ulam type theorem obtained using equivariant methods. |
Keywords: | Borel construction | Borsuk-Ulam type theorems | Dold Theorem | Equilateral triangles on Jordan curve | Equivariant cohomology | Serre spectral sequence | Publisher: | Elsevier | Project: | Advanced methods for cryptology and information processing |
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