Topological Complexity and Related Topics
About this Title
Mark Grant, University of Aberdeen, Aberdeen, United Kingdom, Gregory Lupton, Cleveland State University, Cleveland, OH and Lucile Vandembroucq, University of Minho, Braga, Portugal, Editors
Publication: Contemporary Mathematics
Publication Year: 2018; Volume 702
ISBNs: 978-1-4704-3436-6 (print); 978-1-4704-4405-1 (online)
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28–March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach.
Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik–Schnirelmann category and the Schwarz genus.
This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
Graduate students and research mathematicians interested in algebraic topology and its applications, applications of pure mathematics to engineering, and engineers interested in topology and the motion planning problem.
Table of Contents
- Andrés Ángel and Hellen Colman – Equivariant topological complexities
- José Carrasquel – Rational methods applied to sectional category and topological complexity
- Daniel C. Cohen – Topological complexity of classical configuration spaces and related objects
- Petar Pavešić – A topologist’s view of kinematic maps and manipulation complexity
- Donald M. Davis – On the cohomology classes of planar polygon spaces
- Jean-Paul Doeraene, Mohammed El Haouari and Carlos Ribeiro – Sectional category of a class of maps
- Lucía Fernández Suárez and Lucile Vandembroucq – Q-topological complexity
- Nathan Fieldsteel – Topological complexity of graphic arrangements
- Jesús González, Mark Grant and Lucile Vandembroucq – Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
- Jesús González and Bárbara Gutiérrez – Topological complexity of collision-free multi-tasking motion planning on orientable surfaces
- Mark Grant and David Recio-Mitter – Topological complexity of subgroups of Artin’s braid groups