Regular homotopy classes of singular maps

2005/04/22 by András Juhász, Andras Juhasz
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:57R42 #msc:57R45 #msc:58K30

paper · pdf · doi:10.1112/s0024611504015102

published as Proc. London Math. Soc. (3) 90 (2005) 738-762 · 23 pages, 3 figures

openalex publication_date 2005/04/22 · arxiv created 2005/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two locally generic maps f, g : Mn R2n − 1 are regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if n ≠ 3 and Mn is a closed n-manifold then the regular homotopy class of every locally generic map f : Mn R2n − 1 is completely determined by the number of its singular points provided that f is singular (that is, f is not an immersion). 2000 Mathematics Subject Classification 57R45, 58K30, 57R42.

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