The Equivariant de Rham Theorem in Equivariant Cohomology. - Himes, Zachary. (2017)
Abstract: In cohomology, there is a theorem known as the de Rham theorem which states that real singular cohomology and de Rham cohomology for a smooth manifold are isomorphic rings. Equivariant cohomology is a cohomology theory for a topological space with a continuous group action. Two models for equivariant cohomology are the Borel model and the Cartan model. Henri Cartan proved the equivariant de Rham theorem, which states that when M is a manifold and G is a compact, connected Lie group acting smoothly on M, the equivariant cohomology of M in both models is the same. In this Master's thesis, we describe both models of equivariant cohomolgy and provide an alternate proof of the equivariant de Rham theorem outlined elsewhere in the literature in the case that M has a finite good cover.; Thesis (M.S.)--Tufts University, 2015.; Submitted to the Dept. of Mathematics.; Advisor: Loring Tu.; Committee: Fulton Gonzalez, and Montserrat Teixidor i Bigas.; Keyword: Mathematics.