Topics in applied topology: actions, knots and proteins - Yerolemou, N (2022)
This thesis consists of three parts in which we explore different topics in pure and applied topology; in Part I, we develop an equivariant version of discrete Morse theory compatible with complexes of groups. In Part II, we link discrete Morse theory to knot projections, and in Part III we apply tools from knotoid theory to the study of knotted proteins. The two overall themes running through the thesis are discrete Morse theory and knot theory.