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FUNDAMENTAL GROUPS OF COMPLEMENTS OF PLANE CURVES AND SYMPLECTIC INVARIANTS
 

Summary: FUNDAMENTAL GROUPS OF COMPLEMENTS OF PLANE
CURVES AND SYMPLECTIC INVARIANTS
D. AUROUX, S. K. DONALDSON, L. KATZARKOV, AND M. YOTOV
Abstract. Introducing the notion of stabilized fundamental group for the
complement of a branch curve in CP2
, we define effectively computable invari-
ants 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 cal-
culations on new examples.
1. Introduction
Using approximately holomorphic techniques first introduced in [5], it was shown
in [2] (see also [1]) that compact symplectic 4-manifolds with integral symplectic
class can be realized as branched covers of CP2
and can be investigated using the
braid group techniques developed by Moishezon and subsequently by Moishezon
and Teicher for the study of complex surfaces (see e.g. [13]):
Theorem 1.1 ([2]). Let (X, ) be a compact symplectic 4-manifold, and let L be a
line bundle with c1(L) = 1
2 []. Then there exist branched covering maps fk : X

  

Source: Auroux, Denis - Department of Mathematics, Massachusetts Institute of Technology (MIT)

 

Collections: Mathematics