Symmetric topological complexity of projective and lens spaces

González, Jesús; Landweber, Peter

doi:10.2140/agt.2009.9.473

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Symmetric topological complexity of projective and lens spaces

Jesús González and Peter Landweber

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.

Dedicated to the memory of Bob Stong

Keywords

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

Mathematical Subject Classification 2000

Primary: 55M30, 57R40

References

Publication

Received: 15 January 2009

Revised: 18 February 2009

Accepted: 18 February 2009

Published: 17 March 2009

Authors

Jesús González
Departamento de Matemáticas CINVESTAV–IPN AP 14-740 México City 07000 Mexico

Peter Landweber
Department of Mathematics Rutgers University 110 Frelinghuysen Rd Piscataway, NJ 08854-8019 USA

Volume 9, issue 1 (2009)