Topological robotics in lens spaces
Topological robotics in lens spaces
复制标题
透镜空间中的拓扑机器人
DOI：
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发表时间：
2005
影响因子：
0.8
通讯作者：
Jesús González
中科院分区：
文献类型：
--
作者：
Jesús González
在Farber， Tabachnikov和Yuzvinsky关于投影空间运动规划问题的工作的启发下，我们给出了基于球面间某些广义“斜”映射的透镜空间拓扑复杂度（TC）的估计。最后一个概念与Astey， Davis和作者开发的广义轴向图密切相关，该图描述了可以浸入（2-扭转）透镜空间的最小欧几里得维。因此，这提出了一种更简单的替代“tc方法”来解决真实投影空间的经典浸入问题，其初始阶段我们通过阻碍理论中的技术来解决。
Motivated by the work of Farber, Tabachnikov and Yuzvinsky on the motion planning problem for projective spaces, we give an estimate for the topological complexity (TC) of lens spaces in terms of certain generalized “skew” maps between spheres. This last concept turns out to be closely related to that for a generalized axial map developed by Astey, Davis and the author to characterize the smallest Euclidean dimension where (2-torsion) lens spaces can be immersed. As a result, this suggests an alternative simpler “TC-approach” to the classical immersion problem for real projective spaces, whose initial stages we settle by means of techniques in obstruction theory.