TITLE: electron configuration on manifolds
QUESTION [6 upvotes]: Let $M$ be a Riemannian manifold. For $k\geq 2$, suppose there are $k$ particles whose mass and volume can be regarded as zero and negatively charged with electricity equally. These $k$ particles move on $M$ freely without frictions and mutually repulse from each  other. When these $k$ particles stop at $(x_1,\cdots, x_k)$ and be stable under small disturbance, we just call $(x_1,\cdots,x_k)$ a "electron configuration". The collection of all "electron configuration"s  form the "electron configuration space". 
Question: Are there any reference about the "electron configuration space"?  What formal names of these spaces should I search online?
Question: Any references about the cohomology ring of the "electron configuration space"?

REPLY [6 votes]: There seems to be a considerable body of work on this:
Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds
D.P. Hardin, , E.B. Saff1, 
More by Hardin and Saff. 
http://personales.unican.es/beltranc/archivos/FoCMBeltran2011volume.pdf (Refers to work by Noam Elkies, who will probably have a much more in depth response)
Perhaps most relevant: Papers by Burton Randol and coworkers:
Burton Randol. Stable configurations of repelling points on manifolds. Proc.
Amer. Math. Soc., 142:2769–2773, 2014.
Nechaeva and Randol