Legendrian links and déjà vu moments

A Legendrian link is called a déjà vu link if its components can be connected by a positive Legendrian isotopy but this isotopy cannot be embedded. This is the contact geometric analogue of a pair of events in a spacetime such that there are déjà vu moments on every future-directed timelike path between them. We construct déjà vu links in several geometrically relevant situations and discuss their basic properties.