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Homotopically trivializing the circle in the framed little disks. (English) Zbl 1301.55005
The main theorem proved in this article is that the Deligne-Mumford-Knudsen genus zero operad is a model of the homotopy pushout of the framed little disks operad and a trivial operad, along a circle. Stated and proved in this manner the paper is a formalization of the relationship between the Deligne-Mumford-Knudsen spaces and the frames little disks operad, suggested by Kontsevich in 2005, stating that an action of the framed little disks operad can be extended to an action of the Deligne-Mumford-Knudsen operad, provided the action of the circle is homotopically trivial.
The article is very well written, containing an excellent introduction, an executive summary, and two appendices relaying basic information about model categories and about trees, thus rendering the article, which uses operad theoretic machinery, enjoyable to the savvy reader as well as accessible to the novice.
Reviewer: Ittay Weiss (Suva)

MSC:
55P48 Loop space machines and operads in algebraic topology
18D50 Operads (MSC2010)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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