Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations

Details Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations

2004-10-05

arxiv.org/abs/math/0410119v2

Mathematics

Geometric Topology

18 pages, to appear in Proceedings of the 4th European Congress of Mathematics; v2: corrections to the statements of Theorem 3

Scientific paper

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.

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