Do you have to hold an arcane focus in your hand to use it? Can you wrap it around your wrist or embed it in the pommel of your sword? You need a free hand to manipulate or hold a material component or focus. Some focuses are meant to be worn such as emblems and amulet holy symbols.
Arcane focuses specifically need to be held, the general rules don't account for them being embedded in other objects or worn.
— Dan Dillon 👥 (@Dan_Dillon_1) January 19, 2020
That said, as a DM I'd allow a wizard to wear their crystal focus around their neck as long as they have a free hand to touch/manipulate it when casting.
— Dan Dillon 👥 (@Dan_Dillon_1) January 19, 2020