Small exotic 4-manifolds from lines and quadrics in CP2

Mihajlovic, Stefan (2020) Small exotic 4-manifolds from lines and quadrics in CP2. ACTA MATHEMATICA HUNGARICA. ISSN 0236-5294

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Abstract

We construct potentially new manifolds homeomorphic but not diffeomorphic to CP2#8CP2 and CP2#9CP2 via rational blowdown surgery along certain 4-valent plumbing graphs. This way all the graph classes from \cite{weighted} have a representative which admits a rational blowdown leading to an exotic manifold. We emphasize the simplicity of the constructions which boils down to finding a good configuration of complex lines and quadrics in CP2, and deciding which intersections to blow up.

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