6 citations · 9 across the 6 of their papers we have counts for
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Symplectic 4-manifolds, singular plane curves, and isotopy problems
Denis Auroux
We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying…
Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations
Denis Auroux
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…
Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves
D. Auroux, S. K. Donaldson, L. Katzarkov
We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide…
Fiber sums of genus 2 Lefschetz fibrations
Denis Auroux
Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration…
Fundamental groups of complements of plane curves and symplectic invariants
D. Auroux, S. K. Donaldson, L. Katzarkov +1
Introducing the notion of stabilized fundamental group for the complement of a branch curve in , we define effectively computable invariants of symplectic 4-manifolds that ge…
Symplectic maps to projective spaces and symplectic invariants
Denis Auroux
After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimen…