On certain exotic 4-manifolds of Akhmedov and Park

Details On certain exotic 4-manifolds of Akhmedov and Park On certain exotic 4-manifolds of Akhmedov and Park

2011-02-07

arxiv.org/abs/1102.1376v2

Mathematics

Geometric Topology

10 pages; one reference added

Scientific paper

In an article from 2008, A. Akhmedov and B. D. Park constructed irreducible symplectic 4-manifolds homeomorphic but not diffeomorphic to the manifolds CP^2#3CP^2bar and 3CP^2#5CP^2bar. These manifolds are constructed by using generalized fibre sums. In this note we describe an explicit splitting of the second (co-)homology of these manifolds adapted to their construction as fibre sums. We also calculate the canonical classes of the symplectic structures. This gives a new proof for a formula derived by A. Akhmedov, R. I. Baykur and B. D. Park.

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