Publications de l'Institut Mathématique (Beograd) Vol. 72(86), pp. 2328 (2002) 

VERIFICATION OF ATIYAH'S CONJECTURE FOR SOME NONPLANAR CONFIGURATIONS WITH DIHEDRAL SYMMETRYDragomir \v Z. \DJ okovi\'cDepartment of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, CanadaAbstract: To an ordered $N$tuple of distinct points in the threedimensional Euclidean space, Atiyah has associated an ordered $N$tuple of complex homogeneous polynomials in two variables of degree $N1$, 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 $n=Nm$ points are the vertices of a regular $n$gon whose plane is perpendicular to $L$ and whose centroid lies on $L$. Keywords: Atiyah conjecture Classification (MSC2000): 51M04; 51M16; 70G25 Full text of the article:
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