In this thesis we study graph complexes and their applications to homotopy algebra, differential geometry, and the cohomology of the moduli space of algebraic curves.
The first main topic of this thesis is the study of a new higher dimensional incarnation of one of the most mysterious mathematical structures, the Grothendieck-Teichm¨uller group, using methods and ideas of multi-oriented props and graph complexes.
In Chapter 1, we fix our notation and conventions. We recall the definitions of operads and props following J.-L. Loday and B. Vallette [29], [47]. and D.V. Borisov and Y.I. Manin [8]. We also recall the basic tools of the deformation theory of props developed by B. Vallette and S. Merkulov in [38], and generalize them, rather straightforwardly, to the multi-oriented setting.
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Sergei MERKULOV invites you to join this Webex meeting.
Meeting number (access code): 146 732 901
Meeting password: JHjzCJSc236
Thursday, April 30, 2020
2:00 pm | (UTC+02:00) Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna | 2 hrs
Join meeting: https://unilu.webex.com/unilu/j.php?MTID=mf490546c4955d8976d13303518cc6b0c