| This thesis comprises two main results, one topological, one algebraic. The topological result is that an action of the framed little disks operad and a trivialization of the circle action within it determine an action of the Deligne-Mumford compactification of the moduli space of genus zero curves. The algebraic result is a description of the structure of minimal homotopy Batalin-Vilkovisky algebras and the theorem that in the case that the Batalin-Vilkovisky operator and its higher homotopies are trivial, the remaining algebraic structure is a minimal homotopy hypercommutative algebra. These results are related to one another because the algebraic structures involved are representations of the homology of, respectively, the framed little disks and the Deligne-Mumford compactification. |
