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2009 Symmetric topological complexity of projective and lens spaces
Jesús González, Peter Landweber
Algebr. Geom. Topol. 9(1): 473-494 (2009). DOI: 10.2140/agt.2009.9.473

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.

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Jesús González. Peter Landweber. "Symmetric topological complexity of projective and lens spaces." Algebr. Geom. Topol. 9 (1) 473 - 494, 2009. https://doi.org/10.2140/agt.2009.9.473

Information

Received: 15 January 2009; Revised: 18 February 2009; Accepted: 18 February 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1167.57012
MathSciNet: MR2491582
Digital Object Identifier: 10.2140/agt.2009.9.473

Subjects:
Primary: 55M30, 57R40

Rights: Copyright © 2009 Mathematical Sciences Publishers

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