I will first give an introduction to the Fulton-MacPherson (also called Axelrod-Singer) compactification of the configuration space of n ordered marked points on R^d. Then I will bring your attention to the (almost trivial) observation that the "node smoothing" procedure still works if we formally substitute a finite number of "screen"s -- which are copies of R^ds -- by arbitrary smooth manifolds that (1) are framed; (2) have an "end" that looks like R^d near infinity. I will explain the connection of this observation to the little (d+1)-disk operad action on the classifying space of framed, smooth d-disk bundles (these terminologies will be introduced in the talk) and, if time permits, also its connection to the Lie bracket in graph homology. This is based on joint work in progress with Robin Koytcheff and Sander Kupers.

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