Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 9, Number 1 (2009), 473-494.
Symmetric topological complexity of projective and lens spaces
For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps and (c) the topological complexity are known to be three facets of the same problem. But when it comes to embedding dimension, the classical work of Berrick, Feder and Gitler leaves a small indeterminacy when trying to identify the existence of Euclidean embeddings of these manifolds with the existence of symmetric axial maps. As an alternative we show that the symmetrized version of (c) captures, in a sharp way, the embedding problem. Extensions to the case of even-torsion lens spaces and complex projective spaces are discussed.
Algebr. Geom. Topol., Volume 9, Number 1 (2009), 473-494.
Received: 15 January 2009
Revised: 18 February 2009
Accepted: 18 February 2009
First available in Project Euclid: 20 December 2017
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González, Jesús; Landweber, Peter. Symmetric topological complexity of projective and lens spaces. Algebr. Geom. Topol. 9 (2009), no. 1, 473--494. doi:10.2140/agt.2009.9.473. https://projecteuclid.org/euclid.agt/1513796975