Date of Degree
Geometry and Topology
almost complex structure, six sphere, rational homotopy theory, de rham homotopy
In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on the six sphere and conclude a conjecture about the ordinary homotopy type of that space.
Ferlengez, Bora, "Studying the Space of Almost Complex Structures on a Manifold Using de Rham Homotopy Theory" (2018). CUNY Academic Works.