Symmetrized topological complexity

Abstract

We present upper and lower bounds for symmetrized topological complexity $T{C}^{\Sigma }(X)$ in the sense of Basabe-González-Rudyak-Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square $S{P}^2(X)$. We also show that symmetrized topological complexity coincides with its monoidal version, where the path from a point to itself is required to be constant. Using these results, we calculate the symmetrized topological complexity of all odd spheres.

v2: 15 pages, 2 figures

References in corpus (3)

• Topological Complexity is a Fibrewise L-S Category
• The symmetrized topological complexity of the circle
• Symmetric bi-skew maps and symmetrized motion planning in projective spaces