Decidability of the extension problem for maps into odd-dimensional spheres

2014/01/15 by Lukáš Vokřínek, Vokřínek, Lukáš
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Primary 55Q05 #Secondary 55S35 #cs.CG #math.AT #msc:55Q05 #msc:55S35

paper · pdf · doi:10.48550/arxiv.1401.3758

6 pages

arxiv created 2014/01/15 · arxiv updated 2014/01/17

Abstract

In a recent paper, it was shown that the problem of existence of a continuous map X → Y extending a given map A → Y defined on a subspace A ⊆ X is undecidable, even for Y an even-dimensional sphere. In the present paper, we prove that the same problem for Y an odd-dimensional sphere is decidable. More generally, the same holds for any d-connected target space Y whose homotopy groups π_k Y are finite for k>2d.

Related

• Computing all maps into a sphere
• Extendability of continuous maps is undecidable
• Continuously non-extendable mappings between generalized complex ellipsoids of different dimensions
• On singularities of mappings with a finite length distortion
• A note on Brehm's extension theorem