Erik Lindell: Homotopy Theory of the Framed Little N-disks Operad

Abstract: The subject of this thesis is the real homotopy theory of the framed little n-disks operad. In particular, we study graph complexes that serve as algebraic models for this operad. Such a model was previously found by Anton Khoroshkin and Thomas Willwacher in their paper Real Models for the Framed Little N-disks Operad and in this thesis we prove that a similar, but arguably more useful, complex is also such a model. The thesis is written to be comprehensible for students from the master's level and upwards, so a background on operads is given, as well as a thorough background on the algebraic tools used in the proofs.