What do configuration spaces remember?
by Ben Knudsen
One important perspective in the study of configuration spaces entails viewing them as invariants of the background manifold—but invariants up to what equivalence relation? We will use this question as an excuse to take an ahistorical tour through some of the highlights of the field. By the end, we hope to explain how the question relates to joint work with Kupers, in which we show that 4-dimensional knot theory cannot distinguish smooth structures, answering a question of Viro.