Symmetrized topological complexity
Year: 2017
Type: preprint
Abstract: We present upper and lower bounds for symmetrized topological complexity $TC^Σ(X)$ 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 $SP^2(X)$. 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.
Source: arXiv (Cornell University)
Author: Grant, Mark
Institution: University of Aberdeen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952454282