A geometric classification of immersions of 3-manifolds into 5-space

2005/03/10 by András Juhász, Andras Juhasz
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:57N35 #msc:57R42 #msc:57R45

paper · pdf · doi:10.1007/s00229-005-0543-8

published as manuscripta math. 117, 65-83 (2005) · 17 pages

openalex publication_date 2005/03/10 · arxiv created 2005/06/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

In this paper we define two regular homotopy invariants c and i for immersions of oriented 3-manifolds into R⁵ in a geometric manner. The pair (c(f),i(f)) completely describes the regular homotopy class of the immersion f. The invariant i corresponds to the 3-dimensional obstruction that arises from Hirsch-Smale theory and extends the one defined in [10] for immersions with trivial normal bundle.

Citations

• Regular homotopy classes of singular maps

Related

• Differential 3-knots in 5-space with and without self intersections
• Geometric formulas for Smale invariants of codimension two immersions
• Embeddings in the 3/4 range
• Multiple points of immersions
• Immersions of Surfaces into Aspherical 3-Manifolds