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 $L$.
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
@article{10_2298_PIM0272023D,
author = {Dragomir \v{Z}. {\DJ}okovi\'c},
title = {Verification of {Atiyah's} {Conjecture} for some {Nonplanar} {Configurations} with {Dihedral} {Symmetry}},
journal = {Publications de l'Institut Math\'ematique},
pages = {23 },
year = {2002},
volume = {_N_S_72},
number = {86},
doi = {10.2298/PIM0272023D},
zbl = {1138.51302},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0272023D/}
}
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