Abstract

Turaev's theory of knotoids, besides extending classical knot theory, has proved to provide a  most appropriate mathematical tool for the topological study of proteins, especially knotoids enhanced with bonds. In this talk we shall first present the theory of bonded knots undergoing rigid or non-rigid vertex isotopy. We shall then discuss the basics of the theory of knotoids, we will extend this theory to bonded knotoids and will present applications to the study of proteins. Finally we will present the theory of doubly periodic tangles --appropriate topological objects for the study of filamental structures-- and will introduce the notion of bonded doubly periodic tangles.