Journals / Turkish Journal of Mathematics / 2001 / Cilt: 25 - Sayı: 1
The canonical class of a symplectic four manifold
- Pages
- 137–146
- DOI
- —
Abstract
In this article we present examples of simply connected symplectic 4-manifolds X whose canonical classes are represented by complicated disjoint unions of symplectic submanifolds of X: Theorem. Given finite collections {gi}, {mi}, i=1,...,n, of positive integers, there is a minimal symplectic simply connected 4-manifold X whose canonical class is represented by a disjoint union of embedded symplectic surfaces K ~ Sg1,1 « ... « Sg1,m1 « ... « Sgn,1 «... « S{gn,mn} where Sgi,j is a surface of genus gi. Furthermore, c12(X) = ch(X) - (2+ b) where b= S{i=1}n mi is the total number of connected components of the symplectic representative of the canonical class.
Özet
In this article we present examples of simply connected symplectic 4-manifolds X whose canonical classes are represented by complicated disjoint unions of symplectic submanifolds of X: Theorem. Given finite collections {gi}, {mi}, i=1,...,n, of positive integers, there is a minimal symplectic simply connected 4-manifold X whose canonical class is represented by a disjoint union of embedded symplectic surfaces K ~ Sg1,1 « ... « Sg1,m1 « ... « Sgn,1 «... « S{gn,mn} where Sgi,j is a surface of genus gi. Furthermore, c12(X) = ch(X) - (2+ b) where b= S{i=1}n mi is the total number of connected components of the symplectic representative of the canonical class.