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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    González, Jesús and Velasco, Maurilio 2014. Complex-projective and lens product spaces. Boletín de la Sociedad Matemática Mexicana, Vol. 20, Issue. 2, p. 319.


    García Calcines, J. M. and Vandembroucq, L. 2013. Topological complexity and the homotopy cofibre of the diagonal map. Mathematische Zeitschrift, Vol. 274, Issue. 1-2, p. 145.


    González, Jesús Grant, Mark Torres-Giese, Enrique and Xicoténcatl, Miguel 2013. Topological complexity of motion planning in projective product spaces. Algebraic & Geometric Topology, Vol. 13, Issue. 2, p. 1027.


    GONZÁLEZ, JESÚS VELASCO, MAURILIO and WILSON, W.STEPHEN 2013. BIEQUIVARIANT MAPS ON SPHERES AND TOPOLOGICAL COMPLEXITY OF LENS SPACES. Communications in Contemporary Mathematics, Vol. 15, Issue. 03, p. 1250051.


    COSTA, ARMINDO and FARBER, MICHAEL 2010. MOTION PLANNING IN SPACES WITH SMALL FUNDAMENTAL GROUPS. Communications in Contemporary Mathematics, Vol. 12, Issue. 01, p. 107.


    González, Jesús and Landweber, Peter 2009. Symmetric topological complexity of projective and lens spaces. Algebraic & Geometric Topology, Vol. 9, Issue. 1, p. 473.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 139, Issue 3
  • November 2005, pp. 469-485

Topological robotics in lens spaces

  • JESÚS GONZÁLEZ (a1)
  • DOI: http://dx.doi.org/10.1017/S030500410500873X
  • Published online: 21 October 2005
Abstract

Motivated by the work of Farber, Tabachnikov and Yuzvinsky on the motion planning problem for projective spaces, we give an estimate for the topological complexity (TC) of lens spaces in terms of certain generalized “skew” maps between spheres. This last concept turns out to be closely related to that for a generalized axial map developed by Astey, Davis and the author to characterize the smallest Euclidean dimension where (2-torsion) lens spaces can be immersed. As a result, this suggests an alternative simpler “TC-approach” to the classical immersion problem for real projective spaces, whose initial stages we settle by means of techniques in obstruction theory.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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