## Algebraic & Geometric Topology

### Symmetric topological complexity of projective and lens spaces

#### Abstract

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.

#### Article information

Source
Algebr. Geom. Topol., Volume 9, Number 1 (2009), 473-494.

Dates
Revised: 18 February 2009
Accepted: 18 February 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796975

Digital Object Identifier
doi:10.2140/agt.2009.9.473

Mathematical Reviews number (MathSciNet)
MR2491582

Zentralblatt MATH identifier
1167.57012

#### Citation

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

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