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2012 Estimating the higher symmetric topological complexity of spheres
Roman Karasev, Peter Landweber
Algebr. Geom. Topol. 12(1): 75-94 (2012). DOI: 10.2140/agt.2012.12.75


We study questions of the following type: Can one assign continuously and Σm–equivariantly to any m–tuple of distinct points on the sphere Sn a multipath in Sn spanning these points? A multipath is a continuous map of the wedge of m segments to the sphere. This question is connected with the higher symmetric topological complexity of spheres, introduced and studied by I Basabe, J González, Yu B Rudyak, and D Tamaki. In all cases we can handle, the answer is negative. Our arguments are in the spirit of the definition of the Hopf invariant of a map f:S2n1Sn by means of the mapping cone and the cup product.


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Roman Karasev. Peter Landweber. "Estimating the higher symmetric topological complexity of spheres." Algebr. Geom. Topol. 12 (1) 75 - 94, 2012.


Received: 22 July 2011; Accepted: 1 November 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1244.55013
MathSciNet: MR2889546
Digital Object Identifier: 10.2140/agt.2012.12.75

Primary: 55R80 , 55R91

Keywords: configuration spaces , topological complexity

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 1 • 2012
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