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Examples of 4-manifolds Without Gompf Nuclei

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Abstract

A problem of Kirby (Problem 4.98 in [9]) will be answered in the negative. We show that the 4-manifold X2,2,2 defined below does not contain the Gompf nucleus N2. More generally, we also show the existence of 4-manifolds without Gompf nuclei Nn. The proofs rely on the connection between the smooth topology and the Seiberg-Witten basic classes of a given 4-dimensional manifold M.

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  1. Department of Analysis, Elte TTK, Budapest, Múzeum Krt. 6–8, H-1088

    A. I. Stipsicz

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  1. A. I. Stipsicz
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Stipsicz, A.I. Examples of 4-manifolds Without Gompf Nuclei. Acta Mathematica Hungarica 83, 107–113 (1999). https://doi.org/10.1023/A:1006619704466

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