In the academic year 1984-1985 MSRI ran two simultaneous year-long programs, one in operator algebras and the other in low dimensional topology. The interactions that occurred were at the beginning of a lively and enduring area of mathematics centered around what is now known as TQFT (topological quantum field theory).
MSRI meetings have continued to inspire and unify work in this and neighbouring areas. I will attempt to give a historical survey of this and other closely related areas.

Lecture #12650

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