The space of clouds in an Euclidean space
| dc.creator | Hausmann, Jean-Claude | |
| dc.creator | Rodriguez, Eugenio | |
| dc.date | 2002-07-12 | |
| dc.date.accessioned | 2026-07-07T04:49:39Z | |
| dc.date.available | 2026-07-07T04:49:39Z | |
| dc.description | We study the space $\nua{m}{d}$ of clouds in $\bbr^d$ (ordered sets of $m$ points modulo the action of the group of affine isometries). We show that $\nua{m}{d}$ is a smooth space, stratified over a certain hyperplane arrangement in $\bbr^m$. We give an algorithm to list all the chambers and other strata (this is independent of $d$). With the help of a computer, we obtain the list of all the chambers for $m\leq 9$ and all the strata when $m\leq 8$. As the strata are the product of a polygon spaces with a disk, this gives a classification of $m$-gon spaces for $m\leq 9$. When $d=2,3$, $m=5,6,7$ and modulo reordering, we show that the chambers (and so the different generic polygon spaces) are distinguished by the ring structure of their ${\rm mod} 2$-cohomology. | |
| dc.description | 27 pages; Latex | |
| dc.identifier | https://arxiv.org/abs/math/0207107 | |
| dc.identifier | http://arxiv.org/abs/math/0207107 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64502 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 55R80;57D65;58F05 | |
| dc.title | The space of clouds in an Euclidean space | |
| dc.type | text |