Formulae for order one invariants of immersions and embeddings of surfaces

2003/05/05 by Tahl Nowik, Nowik, Tahl
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Point processes and geometric inequalities #math.GT

paper · pdf · doi:10.48550/arxiv.math/0305070

arxiv created 2003/05/05 · openalex publication_date 2003/05/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The universal order 1 invariant f^U of immersions of a closed orientable surface into R³, whose existence has been established in [N3], takes values in the group G_U = K ⊕ Z/2 ⊕ Z/2 where K is a countably generated free Abelian group. The projections of f^U to K and to the first and second Z/2 factors are denoted f^K, M, Q respectively. An explicit formula for the value of Q on any embedding has been given in [N2]. In the present work we give an explicit formula for the value of f^K on any immersion, and for the value of M on any embedding.

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