Embeddings of Surfaces into 3-Space and Quadruple Points of Regular Homotopies

1999/11/10 by Tahl Nowik, Nowik, Tahl
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.math/9911066

11 pages, 2 figures

arxiv created 1999/11/10 · openalex publication_date 1999/11/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a closed orientable surface. We give an explicit formula for the number mod 2 of quadruple points occurring in any generic regular homotopy between any two regularly homotopic embeddings e,e':F -> R³. The formula is in terms of homological data extracted from the two embeddings.

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