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arxiv: 0907.2671 · v4 · pith:PI2T6Q7Vnew · submitted 2009-07-15 · 🧮 math.SG · math.GT

Generalized fibre sums of 4-manifolds and the canonical class

classification 🧮 math.SG math.GT
keywords manifoldsfibresurfacescanonicalclassclosedderiveembedded
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In this paper 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 in addition the 4-manifolds M and N are symplectic and the surfaces symplectically embedded we derive a formula for the canonical class of the symplectic fibre sum.

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