Dissecting the 2-sphere by immersions

2006/12/27 by Tahl Nowik, Nowik, Tahl · 2 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.math/0612796

openalex publication_date 2006/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The self intersection of an immersion i : S² → R³ dissects S² into pieces which are planar surfaces (unless i is an embedding). In this work we determine what collections of planar surfaces may be obtained in this way. In particular, for every n we construct an immersion i : S² → R³ with 2n triple points, for which all pieces are discs.

Cited by

• An Invariant for Triple-Point-Free Immersed Spheres
• On face angles of tetrahedra with a given base

Related

• Extending Immersions into the Sphere
• Complementary regions for immersions of surfaces
• Polyhedral Embeddings and Immersions of Many Triangulated 2-Manifolds\n with Few Vertices
• The extending surfaces of immersions into surfaces
• Non-separating immersions of spheres and Bing houses