2002/07/12 by Jean-Claude Hausmann, Hausmann, Jean-Claude, Eugenio Rodríguez +2 · 1 citation
Computer Science · Engineering · Mathematics · #55R80 #57D65 #58F05 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Mathematics and Applications #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:55R80 #msc:57D65 #msc:58F05
paper · pdf · doi:10.48550/arxiv.math/0207107
27 pages; Latex
arxiv created 2002/07/12 · openalex publication_date 2002/07/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the space \nuamd of clouds in \bbrd (ordered sets of m points modulo the action of the group of affine isometries). We show that \nuamd is a smooth space, stratified over a certain hyperplane arrangement in \bbrm. 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≤ 9 and all the strata when m≤ 8. As the strata are the product of a polygon spaces with a disk, this gives a classification of m-gon spaces for m≤ 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.