I read about enumerative geometry recently, namely something about the Gromov-Witten, Donaldson-Thomas and Pandharipande-Thomas invariants, and I was trying to see the picture.

It seems like the term "3-fold vertex" appears really often (as well as the word "topological vertex"), and I haven't figure out what it means. It seems like it is something that make sense for any curve counting theory and people really want to compute this thing (and managed to do so in many cases). Can anybody here explain to me what it is and point me to some work that defines and explains this?