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arXiv · 1502.01364

On the Atiyah problem on hyperbolic configurations of four points

Joseph Malkoun
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Abstract

Given a configuration $\mathbf{x}$ of $n$ distinct points in hyperbolic $3$-space $H^3$, Michael Atiyah associated $n$ polynomials $p_1,\ldots,p_n$ of a variable $t \in \mathbb{C}P^1$, of degree $n-1$, and conjectured that they are linearly independent over $\mathbb{C}$, no matter which configuration $\mathbf{x}$ one starts with. We prove this conjecture for $n=4$ in two cases: in case the $4$ points are non-coplanar, and in case one of the points lies in the hyperbolic convex hull of the other three.

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Joseph Malkoun. 2015-02-04. On the Atiyah problem on hyperbolic configurations of four points. https://doi.org/10.1007/s10711-015-0102-8

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