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Estimating the higher
symmetric topological complexity of spheres
Roman Karasev and Peter Landweber |
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Algebraic & Geometric Topology 12 (2012) 75–94
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Abstract |
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We study questions of the following type: Can one assign continuously and –equivariantly to any –tuple of distinct points on the sphere a multipath in spanning these points? A multipath is a continuous map of the wedge of 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 by means of the mapping cone and the cup product. |
Keywords
topological complexity, configuration spaces
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Mathematical Subject Classification 2010
Primary: 55R80, 55R91
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References |
Publication
Received: 22 July 2011
Accepted: 1 November 2011
Published: 8 February 2012
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Authors |
| Roman Karasev | |
| Department of Mathematics Moscow Institute of Physics and Technology Institutskiy per. 9 Dolgoprudny Russia 141700 |
Laboratory of Discrete and
Computational Geometry Yaroslavl’ State University Sovetskaya st. 14 Yaroslavl’ Russia 150000 |
| http://www.rkarasev.ru/en/ | |
| Peter Landweber | |
| Department of Mathematics Rutgers University Piscataway NJ 08854 USA |
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