Symmetrized topological complexity

Mark Grant

doi:10.1142/S1793525319500183

Symmetrized topological complexity

Mark Grant^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

20 Downloads (Pure)

Abstract

We present upper and lower bounds for symmetrized topological complexity TC^Σ(X) in the sense of Basabe–Gonzalez–Rudyak–Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square SP² (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.

Original language	English
Pages (from-to)	387-403
Number of pages	17
Journal	Journal of Topology and Analysis
Volume	11
Issue number	2
Early online date	5 Oct 2017
DOIs	https://doi.org/10.1142/S1793525319500183
Publication status	Published - 1 Jun 2019

Keywords

Topological complexity
topological robotics
equivariant homotopy theory
symmetric products
COHOMOLOGY
CATEGORY

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10.1142/S1793525319500183Licence: Unspecified

Accepted Manuscript
Electronic version of an article published as Grant M. Symmetrized topological complexity. Journal of Topology and Analysis. Vol. 11, No. 02, pp. 387-403 (2019). Available from, DOI: 10.1142/S1793525319500183 © 2017 World Scientific Publishing Company.
Accepted author manuscript, 211 KBLicence: Unspecified

https://arxiv.org/abs/1703.07142Licence: Unspecified

Cite this

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abstract = "We present upper and lower bounds for symmetrized topological complexity TCΣ(X) in the sense of Basabe–Gonzalez–Rudyak–Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square SP2 (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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N2 - We present upper and lower bounds for symmetrized topological complexity TCΣ(X) in the sense of Basabe–Gonzalez–Rudyak–Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square SP2 (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.

AB - We present upper and lower bounds for symmetrized topological complexity TCΣ(X) in the sense of Basabe–Gonzalez–Rudyak–Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of the symmetric square SP2 (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.

KW - Topological complexity

KW - topological robotics

KW - equivariant homotopy theory

KW - symmetric products

KW - COHOMOLOGY

KW - CATEGORY

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UR - http://www.mendeley.com/research/symmetrized-topological-complexity

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M3 - Article

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VL - 11

SP - 387

EP - 403

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 2

ER -

Symmetrized topological complexity

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Mark Grant

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Symmetrized topological complexity

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