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Faculty Publication: Professor of Mathematics Paul Melvin

November 18, 2020

Higher order corks

Authors: Paul Melvin and Hannah Schwartz

Source: Inventiones mathematicae. (2020). https://doi.org/10.1007/s00222-020-01009-x

Publication type: Article

Abstract: It is shown that any finite list of smooth closed simply-connected 4-manifolds homeomorphic to a given one X can be obtained by removing a single compact contractible submanifold (or cork) from X, and then regluing it by powers of a boundary diffeomorphism. We then use this result to 'separate' finite families of corks embedded in a fixed 4-manifold.

Department of Mathematics