Anyone know the name of the effect where the spectator "karate chops" the rope. It is coupled with professors dream? for a fuller routine?

The principle, once mastered, can be used in combination with other rope effects to advantage. Don't limit yourself to "what came in the package."

For example, in one routine I start with a rope tied in a circle like a necklace with several objects there on.
In an attempt to get the objects off to perform magic with, I do several different CR effects.
Finally, with the assistance of a spectator, I get three different lengths of rope (cut on the fly to proper length)
These are stretched into equal lengths so that I can do linking ropes.
The all three are join into a single rope retied into a necklace as in the beginning.

No mention or patter relates to the three ropes becoming equal - I just do it because I need the mis-happened ropes the same.

"Loose Ends" by John Zander you can see a performance on Ytube.

Professor's Nightmare was one of the first tricks in my professional set. I bought it from the magic shop at Busch Gardens. (only later to discover it was already in a book I owned and hadn't read carefully enough)

Ryan Pilling sells some really fun, detailed videos that explain The prof's nightmare and perhaps half a dozen other rope tricks on his site TipsAndTricksForMagicians.com . One of the other tricks is a lovely follow-up to "nightmare," which, curiously, was published years before "nightmare."