Cohomology and Immersed Curves

2008/07/08 by Mario O. Bourgoin, Bourgoin, Mario O.
Computer Science · Mathematics · #57M20 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57M20

paper · pdf · doi:10.48550/arxiv.0807.1311

13 pages, 4 figures

openalex publication_date 2008/07/08 · arxiv created 2012/09/19 · arxiv updated 2012/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new cohomology-theoretic method for classifying generic immersed curves in closed compact surfaces by using Gauss codes. This subsumes a result of J.S. Carter on classifying immersed curves in oriented compact surfaces, and provides a criterion for when an immersion is two-colorable. We note an application to twisted virtual link theory.

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