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Previously, we showed that most of the open-closed topological quantum fieldtheory (TQFT) string operations vanish including all the higher genus TQFToperations, and we described a small list of genus zero open-closed TQFT stringoperations which can be nontrivial. In this paper, we consider open-closedstring operations associated to open-closed cobordisms homeomorphic to discs.These operations constitute the main part of genus zero string operations, andthey include the saddle string operation of two open strings interacting attheir internal points. We show not only that disc string operations areindependent of their half-pair-of-pants decompositions but also that these discstring operations can be computed by \emph{simultaneous} saddle interactions ofincoming open strings at the same point, and they take values in homologyclasses of constant open strings on some closed orientable submanifolds, whichwe will precisely determine. We will also discuss a role played by fundamentalconstant homology classes in open-closed string topology. Our main tools aresaddle interaction diagrams and their deformations.

Open-Closed TQFT String Operations for Disc Cobordisms, Simultaneous Saddle Interactions, and Constant Homology Classes