作为配置空间紧化的结合多面体、环面多面体与置换多面体
代数拓扑
2009-04-23 v2 几何拓扑
摘要
与结合多面体(associahedron)和环面多面体(cyclohedron)的情形一样,置换多面体(permutohedron)也可定义为区间或圆上点集配置空间的适当紧化。该紧化构造赋予置换多面体到环面多面体的投影,以及环面多面体到结合多面体的投影。我们证明,通过这些投影的任意点的原像未必同胚于圆盘(的胞腔分解),但仍是可缩的。我们简要说明了这一结果在从 Goodwillie-Weiss 流形微积分视角研究纽结空间中的应用。
引用
@article{arxiv.math/0612591,
title = {Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces},
author = {P. Lambrechts and V. Tourtchine and I. Volic},
journal= {arXiv preprint arXiv:math/0612591},
year = {2009}
}
备注
27 pages The new version gives a more detailed exposition for the projection from the cyclohedron to the associahedron as maps of compactifications of configuration spaces. We also develop a similar picture for the projection from the permutohedron to the cyclohedron/associahedron