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.
Survey Articles: A. Angel and H. Colman, Equivariant topological
complexities
J. Carrasquel, Rational methods applied to sectional category and topological
complexity
D. C. Cohen, Topological complexity of classical configuration spaces and
related objects
P. Pavesic, A topologist's view of kinematic maps and manipulation
complexity
Research Articles: D. M. Davis, On the cohomology classes of planar polygon
spaces
J.-P. Doeraene, M. El Haouari, and C. Ribeiro, Sectional category of a class
of maps
L. Fernandez Suarez and L. Vandembroucq, Q-topological complexity
N. Fieldsteel, Topological complexity of graphic arrangements
J. Gonzalez, M. Grant, and L. Vandembroucq, Hopf invariants, topological
complexity, and LS-category of the cofiber of the diagonal map for two-cell
complexes
J. Gonzalez and B. Gutierrez, Topological complexity of collision-free
multi-tasking motion planning on orientable surfaces
M. Grant and D. Recio-Mitter, Topological complexity of subgroups of Artin's
braid groups.
Mark Grant, University of Aberdeen, United Kingdom.
Gregory Lupton, Cleveland State University, OH.
Lucile Vandembroucq, University of Minho, Braga, Portugal.
