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Topological robotics in lens spaces

Published online by Cambridge University Press:  21 October 2005

JESÚS GONZÁLEZ
Affiliation:
Departamento de Matemáticas, CINVESTAV–IPN, México D.F.07000. e-mail: jesus@math.cinvestav.mx

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.

Type
Research Article
Copyright
2005 Cambridge Philosophical Society

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