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Topological complexity of real Grassmannians

Part of: Classical Topics in Algebraic Topology Operations and obstructions

Published online by Cambridge University Press:  12 January 2021

Petar Pavešić
Petar Pavešić*
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Jadranska 21, 1000, Slovenija (petar.pavesic@fmf.uni-lj.si)
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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

Topological complexityLusternik–Schnirelmann categoryStiefel–Whitney classesGrassmann manifoldzero divisor cup-length

MSC classification

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
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
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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Footnotes

Supported by the Slovenian Research Agency program P1-0292 and grants N1-0083, N1-0064.

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