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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