The moduli space of points in quaternionic projective space
arXiv:1705.06458
Abstract
Let $\mathcal{M}(n,m;\F \bp^n)$ be the configuration space of -tuples of pairwise distinct points in $\F \bp^n$, that is, the quotient of the set of -tuples of pairwise distinct points in $\F \bp^n$ with respect to the diagonal action of ${\rm PU}(1,n;\F)$ equipped with the quotient topology. It is an important problem in hyperbolic geometry to parameterize $\mathcal{M}(n,m;\F \bp^n)$ and study the geometric and topological structures on the associated parameter space. In this paper, by mainly using the rotation-normalized and block-normalized algorithms, we construct the parameter spaces of both $\mathcal{M}(n,m; \bhq)$ and $\mathcal{M}(n,m;\bp(V_+))$, respectively.
31 pages