2012/11/05 by Larry Guth, Guth, Larry
Mathematics · #53C23 #Advanced Topology and Set Theory #Biology #Combinatorics #Contraction (grammar) #Differential Geometry (math.DG) #Dilation (metric space) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Topology (electrical circuits) #Unit (ring theory) #Unit sphere #math.DG #math.GT #msc:53C23
paper · pdf · doi:10.48550/arxiv.1211.1057
82 pages. Typos corrected. Reference added to a recent paper of Wenger and Young. Accepted for publication in Geometric and Functional Analysis
openalex publication_date 2012/11/05 · arxiv created 2013/05/29 · arxiv updated 2013/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct homotopically non-trivial maps from the unit m-sphere to the unit (m-1)-sphere with arbitrarily small k-dilation for each k greater than (m + 1)/2. We prove that homotopically non-trivial maps from the unit m-sphere to the unit (m-1)-sphere cannot have arbitrarily small k-dilation for k less than or equal to (m + 1)/2.