Fake 4-ball

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In mathematics, a fake 4-ball is a compact contractible topological 4-manifold. Michael Freedman proved that every three-dimensional homology sphere bounds a fake 4-ball. His construction involves the use of Casson handles and so does not work in the smooth category.


  • Alexandru Scorpan, The Wild World of 4-Manifolds, American Mathematical Society, ISBN 0-8218-3749-4