Algebraic & Geometric Topology 9 (2009) 473–494

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.

Keywords

symmetric topological complexity, Euclidean embedding, biequivariant map, symmetric axial map, projective space, lens space

Mathematical Subject Classification

Primary: 55M30, 57R40

References

Publication

Received: 15 January 2009
Revised: 18 February 2009
Accepted: 18 February 2009
Published: 17 March 2009

Authors