Generalized fibre sums of 4-manifolds and the canonical class

Details Generalized fibre sums of 4-manifolds and the canonical class Generalized fibre sums of 4-manifolds and the canonical class

2009-07-15

arxiv.org/abs/0907.2671v2

Mathematics

Symplectic Geometry

55 pages, 1 figure, small improvements

Scientific paper

In this article we determine the integral homology and cohomology groups of a closed 4-manifold X obtained as the generalized fibre sum of two closed 4-manifolds M and N along embedded surfaces of genus g and self-intersection zero. If the homologies of the 4-manifolds are torsion free and the surfaces represent indivisible homology classes, we derive a formula for the intersection form of X. If the 4-manifolds M and N are symplectic and the surfaces symplectically embedded we also derive a formula for the canonical class of the symplectic fibre sum.

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