Symmetric topological complexity of projective and lens spaces
نویسندگان
چکیده
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. This paper describes the corresponding relationship between the symmetrized versions of (b) and (c) to the Euclidean embedding dimension of projective spaces. Extensions to the case of 2e torsion lens spaces and complex projective spaces are discussed. 2000 MSC: 55M30, 57R40.
منابع مشابه
Symmetric Topological Complexity as the First Obstruction in Goodwillie’s Euclidean Embedding Tower for Real Projective Spaces
As a first goal, it is explained why the Goodwillie-Weiss calculus of embeddings offers new information about the Euclidean embedding dimension of Pm only for m ≤ 15. Concrete scenarios are described in these low-dimensional cases, pinpointing where to look for potential—but critical— high-order obstructions in the corresponding Taylor towers. For m ≥ 16, the relation TC(Pm) ≥ n is translated i...
متن کاملPseudo Ricci symmetric real hypersurfaces of a complex projective space
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
متن کاملFinal Review: Mathematics 432/532
• Spaces can be constructed by gluing simple things together. We constructed projective spaces, Klein bottles, and lens spaces that way. The simple pieces live in Rn, but the new objects usually don’t. (To be more precise, it is irrelevant and distracting to find an embedding of the new objects into Rn.) We introduced topological spaces and particularly the quotient topology so we could talk ab...
متن کاملFlag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
متن کامل