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Tag: Atiyah-Sutcliffe conjectures

The Atiyah-Sutcliffe determinant

The Atiyah-Sutcliffe determinant

This post is a continuation of my series of posts, which includes previous posts such as “the spin-statistics theorem and the Berry-Robbins problem” and “the Atiyah problem on configurations”. I will make use of notation introduced there, particularly in the latter post. I will explain in this post, how to define the Atiyah-Sutcliffe normalized determinant function, which is a smooth complex-valued function on $C_n(\mathbb{R}^3)$. Given a configuration $\mathbf{x} = (\mathbf{x}_1, \ldots, \mathbf{x}_n) \in C_n(\mathbb{R}^3)$ of $n$ distinct points in $\mathbb{R}^3$,…

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The Atiyah Problem on Configurations

The Atiyah Problem on Configurations

This post is a continuation of my previous post “the spin-statistics theorem and the Berry-Robbins problem”. The reader is referred to that post to understand the origins of the Atiyah problem on configurations and the Atiyah-Sutcliffe conjectures. Let $C_n(\mathbb{R}^3)$ denote the configuration space of $n$ distinct points in $\mathbb{R}^3$. Given $\mathbf{x} = (\mathbf{x}_1,\ldots,\mathbf{x}_n) \in C_n(\mathbb{R}^3)$, so that each $\mathbf{x}_i \in \mathbb{R}^3$, for $i = 1, \ldots, n$ and the $\mathbf{x}_i$ are distinct, we will associate to the configuration $\mathbf{x}$ $n$…

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