Date of Award
Master of Arts in Mathematics
First Reader/Committee Chair
This thesis will discuss the de Rham cohomology, homotopy invariance and the Mayer-Vietoris sequence. First the necessary information for this thesis is discussed such as differential p-forms, the exterior derivative as well as pull back of a map. The de Rham cohomology is defined explicitly, some properties of the de Rham cohomology will also be discussed. It will be shown that the de Rham cohomology is in fact a homotopy invariant as well as some examples using homotopy invariance are provided. Finally the Mayer-Vietoris sequence will be established, an example of using the Mayer-Vietoris sequence to compute the de Rham cohomology of groups of spheres is provided.
Cox, Stacey Elizabeth, "de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence" (2022). Electronic Theses, Projects, and Dissertations. 1426.