Symmetric topological complexity of projective and lens spaces

González, Jesús¹ ; Landweber, Peter²

¹Departamento de Matemáticas, CINVESTAV–IPN, AP 14-740 México City 07000, Mexico
²Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd, Piscataway, NJ 08854-8019, USA

Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 473-494

Résumé

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.

Détail

DOI : 10.2140/agt.2009.9.473

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

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