Publications de l'Institut Mathématique (Beograd)Vol. 72(86), pp. 23-28 (2002)
|
|
Publications de l'Institut Mathématique (Beograd) Vol. 72(86), pp. 23-28 (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 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 $L$. Keywords: Atiyah conjecture Classification (MSC2000): 51M04; 51M16; 70G25 Full text of the article:
Electronic version published on: 23 Nov 2003. This page was last modified: 24 Nov 2003.
© 2003 Mathematical Institute of the Serbian Academy of Science and Arts
|