Anigi is both a place and an event alluded to several times in A Thread Between The Stars. Caused by Valcen six billion years prior to the events in the aforementioned book, it resulted in his ostracism from his fellow Threadwielders - something Jeneth considers the minimally just punishment.
Its name relates to the word nigi (home, shelter).
(image courtesy of Concavenator; not originally conceived as Anigi, but sufficient likeness that the author decided to nab it (with his permission))