A moduli space for rational homotopy types with the same homotopy lie algebra
Zawodniak, Matthew David
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One of the major goals of rational homotopy theory is to classify the rational homotopy types of simply connected topological spaces, up to weak equivalence. In 1969, Quillen published a paper in which he showed that this was equivalent to studying many other homotopy categories. This led to a model for the rational homotopy types of topological spaces with the same cohomology algebra, and eventually produced a moduli space. However, a moduli space for topological spaces with the same homotopy groups has not been thoroughly developed or produced, even though the models can be constructed very nicely. This dissertation describes the Lie models used to represent rational homotopy types of simply connected topological spaces. Then, the deformation theory is developed. Finally, a moduli space for rational homotopy types with the same homotopy Lie algebra is described and justified.