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Topological complexity of real Grassmannians

Published online by Cambridge University Press:  12 January 2021

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

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.

Type
Research Article
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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