Mathematics Colloquia and Seminars

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One well-known strategy for distinguishing smooth structures on closed 4-manifolds is to produce a knot $K$ in $S^3$ which is (smoothly) slice in one smooth filling $W$ of $S^3$ but not slice in some homeomorphic smooth filling $W’$. There are many techniques for distinguishing smooth structures on complicated closed 4-manifolds, but this strategy stands out for it’s potential to work for 4-manifolds $W$ with very little algebraic topology. However, this strategy had never actually been used in practice, even for complicated $W$. I’ll discuss joint work with Manolescu and Marengon which gives the first application of this strategy. I’ll also discuss joint work with Manolescu which gives a systematic approach towards using this strategy to produce exotic definite closed 4-manifolds.