Duals of non-zero square

Hannah R. Schwartz

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arXiv · 2012.05939

Duals of non-zero square

Hannah R. Schwartz

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Abstract

In this short note, for each non-zero integer n, we construct a 4-manifold containing a smoothly concordant pair of spheres with a common dual of square n but no automorphism carrying one sphere to the other. Our examples, besides showing that the square zero assumption on the dual is necessary in Gabai's and Schneiderman-Teichner's versions of the 4D Light Bulb Theorem, have the interesting feature that both the Freedman-Quinn and Kervaire-Milnor invariant of the pair of spheres vanishes. The proof gives a surprising application of results due to Akbulut-Matveyev and Auckly-Kim-Melvin-Ruberman pertaining to the well-known Mazur cork.

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Hannah R. Schwartz. 2020-12-10. Duals of non-zero square. https://arxiv.org/abs/2012.05939

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