  To open-closed cobordism surfaces, open-closed string topology associates
topological quantum field theory (TQFT) operations, namely string operations,
which depend only on homeomorphism types of surfaces and which satisfy the
sewing property. We show that most TQFT string operations vanish in open-closed
string topology. We describe those open-closed cobordisms with vanishing string
operations, and give a short list of open-closed cobordisms with possibly
nontrivial string operations.
