{"paper":{"title":"Deformation of Properly Discontinuous Actions of Z^k on R^{k+1}","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"Salma Nasrin, Toshiyuki Kobayashi","submitted_at":"2006-03-14T05:57:23Z","abstract_excerpt":"We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations.\n  A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of discontinuous groups, we introduce the concepts from a group theoretic perspective, and focus on `stability' and `local rigidity' of discontinuous groups.\n  As a test case, we give an explicit description of the deformation space of Z^k acting properly discontinuously on R^{k+1} by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603318","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}