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](https://en.wikipedia.org/wiki/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"?



electron configuration on manifolds
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://www.math.vanderbilt.edu/~esaff/texts/201.pdf) 


<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](http://arxiv.org/abs/1410.3804)


