2001/03/25 by Tahl Nowik, Nowik, Tahl
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #math.GT
paper · pdf · doi:10.48550/arxiv.math/0103157
6 figures
arxiv created 2001/03/25 · openalex publication_date 2001/03/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify all order one invariants of immersions of a closed orientable surface F into R3, with values in an arbitrary Abelian group G. We show that for any F and G and any regular homotopy class A of immersions of F into R3, the group of all order one invariants on A is isomorphic to G^ℵ0 ⊕ B ⊕ B where G^ℵ0 is the group of all functions from a set of cardinality ℵ0 into G and B=x∈ G : 2x=0. Our work includes foundations for the study of finite order invariants of immersions of a closed orientable surface into R3, analogous to chord diagrams and the 1-term and 4-term relations of knot theory.