Farley-Sabalka's Morse-Theory Model and the Higher Topological Complexity of Ordered Configuration Spaces on Trees

被引：1

作者：

Aguilar-Guzman, Jorge ^{[1
]}

Gonzalez, Jesus ^{[1
]}

Hoekstra-Mendoza, Teresa ^{[1
]}

机构：

[1] Ctr Invest & Estudios Avanzados IPN, Dept Matemat, Av Inst Politecn Nacl 2508, Mexico City 07000, DF, Mexico

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2022年 / 67卷 / 01期

关键词：

Discretized configuration space on a tree; Discrete Morse theory; Farley-Sabalka gradient field; Topological complexity;

D O I：

10.1007/s00454-021-00306-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Using the ordered analogue of Farley-Sabalka's discrete gradient field on the configuration space of a graph, we unravel a levelwise behavior of the generators of the pure braid group on a tree. This allows us to generalize Farber's equivariant description of the homotopy type of the configuration space on a tree on two particles. The results are applied to the calculation of all the higher topological complexities of ordered configuration spaces on trees on any number of particles.

引用

页码：258 / 286

页数：29