2004/10/05 by Denis Auroux, Auroux, Denis
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.math/0410119
18 pages, to appear in Proceedings of the 4th European Congress of Mathematics; v2: corrections to the statements of Theorem 3.8 and Lemma 4.5
openalex publication_date 2004/10/05 · arxiv created 2005/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The topology of symplectic 4-manifolds is related to that of singular plane curves via the concept of branched covers. Thus, various classification problems concerning symplectic 4-manifolds can be reformulated as questions about singular plane curves. Moreover, using braid monodromy, these can in turn be reformulated in the language of braid group factorizations. While the results mentioned in this paper are not new, we hope that they will stimulate interest in these questions, which remain essentially wide open.