Symmetrized topological complexity

Mark Grant

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arXiv · 1703.07142

Symmetrized topological complexity

Mark Grant

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Abstract

We present upper and lower bounds for symmetrized topological complexity $TC^\Sigma(X)$ in the sense of Basabe-Gonz\'alez-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.

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Mark Grant. 2017-03-21. Symmetrized topological complexity. https://arxiv.org/abs/1703.07142

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