Symmetric topological complexity of projective and lens spaces

Details Symmetric topological complexity of projective and lens spaces Symmetric topological complexity of projective and lens spaces

2008-09-04

arxiv.org/abs/0809.0816v5

Mathematics

Algebraic Topology

Paper reorganized for clarity in exposition

Scientific paper

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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