That he smugly invites Spock to share in the knowledge of Genesis does not mean that he himself had any previous knowledge of the project, either. He could have googled it himself right after hearing the novel and unfamiliar name in Marcus' SOS.
It is equally possible that he knew, though. Perhaps it was knowledge available to flag officers but not starship captains? Perhaps he indeed was involved in some fashion? Perhaps he and Carol still had a thing going, and she leaked state secrets at tender moments, or when trying to impress Jim? The simplest assumption is that Kirk didn't know, though. But perhaps that's not the dramatically most pleasing one.
Timo Saloniemi
It is equally possible that he knew, though. Perhaps it was knowledge available to flag officers but not starship captains? Perhaps he indeed was involved in some fashion? Perhaps he and Carol still had a thing going, and she leaked state secrets at tender moments, or when trying to impress Jim? The simplest assumption is that Kirk didn't know, though. But perhaps that's not the dramatically most pleasing one.
Timo Saloniemi