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Topological complexity of real Grassmannians
Published online by Cambridge University Press: 12 January 2021
Abstract
We use some detailed knowledge of the cohomology ring of real Grassmann manifolds Gk(ℝn) to compute zero-divisor cup-length and estimate topological complexity of motion planning for k-linear subspaces in ℝn. In addition, we obtain results about monotonicity of Lusternik–Schnirelmann category and topological complexity of Gk(ℝn) as a function of n.
Keywords
MSC classification
Secondary:
55S40: Sectioning fiber spaces and bundles
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 2013 - 2029
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
Footnotes
Supported by the Slovenian Research Agency program P1-0292 and grants N1-0083, N1-0064.
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