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arXiv · 0808.3841

Tetrahedra on deformed spheres and integral group cohomology

Pavle V. M. Blagojevic·Günter M. Ziegler
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Abstract

We show that for every injective continuous map f: S^2 --> R^3 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 R^3. 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.

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Pavle V. M. Blagojevic, Günter M. Ziegler. 2008-08-28. Tetrahedra on deformed spheres and integral group cohomology. https://arxiv.org/abs/0808.3841

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