Trends in Topological Combinatorics

This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of the subject. That introduction is followed by 5 chapters, where the main body of research is presented, and 4 appendices, where various standard tools and notations, which we use throughout the text, are collected.