On the Atiyah problem on hyperbolic configurations of four points

@article{Malkoun2016OnTA,
  title={On the Atiyah problem on hyperbolic configurations of four points},
  author={Joseph Malkoun},
  journal={Geometriae Dedicata},
  year={2016},
  volume={180},
  pages={287-292}
}
Given a configuration $$\mathbf {x}$$x of n distinct points in hyperbolic 3-space $$H^3$$H3, Sir Michael Atiyah associated n polynomials $$p_1,\ldots ,p_n$$p1,…,pn of a variable $$t \in \mathbb {C}P^1$$t∈CP1, of degree $$n-1$$n-1, and conjectured that they are linearly independent over $$\mathbb {C}$$C, no matter which configuration $$\mathbf {x}$$x one starts with. We prove this conjecture for almost all hyperbolic configurations of four points, namely for a subset of the $$n=4$$n=4 hyperbolic… CONTINUE READING
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