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CATEGORY AND TOPOLOGICAL COMPLEXITY OF THE CONFIGURATION SPACE
$F(G\times \mathbb{R}^{n},2)$
Published online by Cambridge University Press: 24 May 2019
Abstract
The Lusternik–Schnirelmann category cat and topological complexity TC are related homotopy invariants. The topological complexity TC has applications to the robot motion planning problem. We calculate the Lusternik–Schnirelmann category and topological complexity of the ordered configuration space of two distinct points in the product $G\times \mathbb{R}^{n}$ and apply the results to the planar and spatial motion of two rigid bodies in
$\mathbb{R}^{2}$ and
$\mathbb{R}^{3}$ respectively.
Keywords
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 100 , Issue 3 , December 2019 , pp. 507 - 517
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
The author wishes to acknowledge support for this research from grant no. 2016/18714-8, São Paulo Research Foundation (FAPESP).