Authors: Blagojević, Pavle 
Ziegler, Günter M.
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Tetrahedra on deformed spheres and integral group cohomology
Journal: Electronic Journal of Combinatorics
Volume: 16
Issue: 2
First page: 1
Last page: 11
Issue Date: 10-Jun-2009
Rank: M22
ISSN: 1077-8926
DOI: 10.37236/82
We show that for every injective continuous map f:S2→R3 there are four distinct points in the image of f such that the convex hull is a tetrahedron with the property that two opposite edges have the same length and the other four edges are also of equal length. This result represents a partial result for the topological Borsuk problem for R3. Our proof of the geometrical claim, via Fadell–Husseini index theory, provides an instance where arguments based on group cohomology with integer coefficients yield results that cannot be accessed using only field coefficients.
Publisher: E-JC
Project: Advanced methods for cryptology and information processing 

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