Tetrahedra on deformed spheres and integral group cohomology

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dc.creatorBlagojevic, Pavle V. M.
dc.creatorZiegler, Günter M.
dc.date2008-08-28
dc.date.accessioned2026-07-07T09:59:03Z
dc.date.available2026-07-07T09:59:03Z
dc.descriptionWe 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.
dc.description8 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0808.3841
dc.identifierhttp://arxiv.org/abs/0808.3841
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167897
dc.subjectAlgebraic Topology
dc.subjectMetric Geometry
dc.subject55N25; 52C35
dc.titleTetrahedra on deformed spheres and integral group cohomology
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