Fundamental groups of complements of plane curves and symplectic invariants

2002/03/18 by Denis Auroux, D. Auroux, Simon Donaldson +9
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.AG #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.math/0203183

34 pages, 9 figures

arxiv created 2002/03/18 · openalex publication_date 2002/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Introducing the notion of stabilized fundamental group for the complement of a branch curve in CP², we define effectively computable invariants of symplectic 4-manifolds that generalize those previously introduced by Moishezon and Teicher for complex projective surfaces. Moreover, we study the structure of these invariants and formulate conjectures supported by calculations on new examples.

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