Geodesic
Verification of Atiyah's Conjecture for some Nonplanar Configurations with Dihedral Symmetry
Publications de l'Institut Mathématique, _N_S_72 (2002) no. 86, p. 23 .

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To an ordered $N$-tuple of distinct points in the three-dimensional Euclidean space, Atiyah has associated an ordered $N$-tuple of complex homogeneous polynomials in two variables of degree $N-1$, each determined only up to a scalar factor. He has conjectured that these polynomials are linearly independent. In this note it is shown that Atiyah's conjecture is true if $m$ of the points are on a line $L$ and the remaining $n=N-m$ points are the vertices of a regular $n$-gon whose plane is perpendicular to $L$ and whose centroid lies on $L$.
DOI : 10.2298/PIM0272023D
Classification : 51M04 51M16 70G25 
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     title = {Verification of {Atiyah's} {Conjecture} for some {Nonplanar} {Configurations} with {Dihedral} {Symmetry}},
     journal = {Publications de l'Institut Math\'ematique},
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Dragomir Ž. Đoković. Verification of Atiyah's Conjecture for some Nonplanar Configurations with Dihedral Symmetry. Publications de l'Institut Mathématique, _N_S_72 (2002) no. 86, p. 23 . doi : 10.2298/PIM0272023D. http://geodesic.mathdoc.fr/articles/10.2298/PIM0272023D/

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