An introduction to Topology in soft and biological matter

Abstract

The last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterization of knots in single polymers and proteins to that of whole chromosomes and polymer melts. At the same time, considerable advances have been made in the description of the interplay between topological and physical properties in complex fluids, with the development of techniques that now allow researchers to control the formation of and interaction between defects in diverse classes of liquid crystals. Thanks to technological progress and the integration of experiments with increasingly sophisticated numerical simulations, topological biological and soft matter is a vibrant area of research attracting scientists from a broad range of disciplines. Here we present a comprehensive and coherent introduction to the topological properties of polymers and of continuum materials, highlighting the underlying common aspects concerning the emergence, characterization, and effects of topological objects in different systems. The second half of the talk will be dedicated to the presentation of a selected set of examples including polymer melts, the kinetoplast DNA, a natural 2D topological material made of thousands of interlocked DNA minirings, entangled proteins, and the emergence and effect of topological constraints in complex fluids.