Abstract
Smoothing theory translates the question of how many smooth or PL structures a high-dimensional manifold admits into algebraic topology. While it does not apply verbatim in dimension four, the high dimensional theory makes partial predictions about smoothings of 4-manifolds. I will discuss the extent to which they come true, and some of the resulting exotic phenomena. Based on joint work with Daher, Kasprowski, Nagy, Orson, and Randal-Williams.
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