Duals of non-zero square
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Publication:6355773
DOI10.4310/MRL.2022.V29.N1.A8arXiv2012.05939MaRDI QIDQ6355773
Publication date: 10 December 2020
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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