|
|||||
|
|
|
|
|
|
|
|
|
Higher topological
complexity and its symmetrization
Ibai Basabe, Jesús González, Yuli B Rudyak and Dai Tamaki |
|
Algebraic & Geometric Topology 14 (2014) 2103–2124
|
Abstract |
|
We develop the properties of the sequential topological complexity , a homotopy invariant introduced by the third author as an extension of Farber’s topological model for studying the complexity of motion planning algorithms in robotics. We exhibit close connections of to the Lusternik–Schnirelmann category of cartesian powers of , to the cup length of the diagonal embedding , and to the ratio between homotopy dimension and connectivity of . We fully compute the numerical value of for products of spheres, closed –connected symplectic manifolds and quaternionic projective spaces. Our study includes two symmetrized versions of . The first one, unlike Farber and Grant’s symmetric topological complexity, turns out to be a homotopy invariant of ; the second one is closely tied to the homotopical properties of the configuration space of cardinality- subsets of . Special attention is given to the case of spheres. |
Keywords
Lusternik–Schnirelmann category, Švarc genus, topological
complexity, motion planning, configuration spaces
|
Mathematical Subject Classification 2010
Primary: 55M30
Secondary: 55R80
|
References |
Publication
Received: 31 August 2013
Accepted: 4 January 2014
Published: 28 August 2014
|
Authors |
| Ibai Basabe | |
| Department of Mathematics University of Florida 358 Little Hall Gainesville, FL 32611-8105 USA |
|
| Jesús González | |
| Departamento de Matemáticas CINVESTAV-IPN A.P. 14-740 México City 07000 México |
|
| Yuli B Rudyak | |
| Department of Mathematics University of Florida 358 Little Hall Gainesville, FL 32611-8105 USA |
|
| Dai Tamaki | |
| Department of Mathematical
Sciences Shinshu University Matsumoto 390-8621 Japan |
|
|
