Geodesic
Proof of Atiyah's conjecture for two special types of configurations
The electronic journal of linear algebra, Tome 9 (2002), pp. 132-137.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: To an ordered N-tuple (x1, . . . , xN ) of distinct points in the three-dimensional Euclidean space Atiyah has associated an ordered N-tuple of complex homogeneous polynomials (p1, . . . , pN ) in two variables x, y of degree N - 1, each pi 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 for two special configurations of N points. For one of these configurations, it is shown that a stronger conjecture of Atiyah and Sutcliffe is also valid.
Classification : 51M04, 51M16, 70G25
Keywords: atiyah's conjecture, Hopf map, configuration of N points in the three-dimensional Euclidean space, complex projective line 
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     author = {Djokovi\'c, Dragomir \v{Z}.},
     title = {Proof of {Atiyah's} conjecture for two special types of configurations},
     journal = {The electronic journal of linear algebra},
     pages = {132--137},
     publisher = {mathdoc},
     volume = {9},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2002__9__a10/}
}
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Djoković, Dragomir Ž. Proof of Atiyah's conjecture for two special types of configurations. The electronic journal of linear algebra, Tome 9 (2002), pp. 132-137. http://geodesic.mathdoc.fr/item/ELA_2002__9__a10/