Symmetrized topological complexity

被引：5

作者：

Grant, Mark ^{[1
]}

机构：

[1] Univ Aberdeen, Inst Math, Fraser Noble Bldg, Aberdeen AB24 3UE, Scotland

来源：

JOURNAL OF TOPOLOGY AND ANALYSIS | 2019年 / 11卷 / 02期

关键词：

Topological complexity; topological robotics; equivariant homotopy theory; symmetric products; COHOMOLOGY; CATEGORY;

D O I：

10.1142/S1793525319500183

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present upper and lower bounds for symmetrized topological complexity TC Sigma(X) in the sense of Basabe-Gonzalez-Rudyak-Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square SP2(X). We also show that symmetrized topological complexity coincides with its monoidal version, where the path from a point to itself is required to be constant. Using these results, we calculate the symmetrized topological complexity of all odd spheres.

引用

页码：387 / 403

页数：17

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