Homotopically trivializing the circle in the framed little disks

摘要

This paper confirms the following suggestion of Kontsevich. In the appropriate derived sense, an action of the framed little disks operad and a trivialization of the circle action is the same information as an action of the Deligne–Mumford–Knudsen operad. This improves an earlier result of the author and Bruno Vallette.