Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packed to interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.