math_groups_discgeom

Tetrahedra on deformed spheres and integral group cohomology

Pavle V. M. Blagojević and Günter M. Ziegler— 2009

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.

TitelTetrahedra on deformed spheres and integral group cohomology
VerfasserPavle V. M. Blagojević and Günter M. Ziegler
Datum2009
Quelle/n
Erschienen inElectronic J. Combinatorics, volume 16(2) (Björner Festschrift
ArtText