We say that two smooth 4manifolds are exotic if they are homemorphic but not diffeomorphic. Wall's theorem, proven in 1964, says that when the given 4manifolds are simplyconnected, they are always diffeomorphic after sufficiently many stabilizations, i.e. connectedsumming with S^2 \times S^2, but whether we need more than one stabilization remained mysterious for almost sixty years. In this talk, I will present the first example of an exotic pair of simplyconnected 4manifolds with common boundary which stays exotic after one stabilization. This talk is based on my work arXiv:2210.07510, which involves a careful argument involving borderedinvolutive techniques in Heegaard Floer theory, pioneered by arXiv:2202.12500 and arXiv:2207.11870 by K. and K.Park.
Monday, December 4, 2023  3:30pm
Sungkyung Kang
University of Oxford
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