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CATEGORY AND TOPOLOGICAL COMPLEXITY OF THE CONFIGURATION SPACE $F(G\times \mathbb{R}^{n},2)$

Part of: Fiber spaces and bundles Homotopy theory Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  24 May 2019

CESAR A. IPANAQUE ZAPATA Open the ORCID record for CESAR A. IPANAQUE ZAPATA [Opens in a new window]
CESAR A. IPANAQUE ZAPATA*
Affiliation:
Departamento de Matemática, Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação - USP, Avenida Trabalhador São-carlense, 400 - Centro CEP: 13566-590, São Carlos - SP, Brasil email cesarzapata@usp.br
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Abstract

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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

configuration spacescup-lengthzero-divisor cup-lengthtopological complexityLusternik–Schnirelmann category

MSC classification

Primary: 55R80: Discriminantal varieties, configuration spaces
Secondary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space 55P10: Homotopy equivalences
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).

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