In a future, caste based society a man is caught leading a double life and marrying outside of his caste. In exchange for staying with his family, he agrees to travel back in time to prevent a particular caste from ever coming into existence. The critical event that needs to be changed is the Cuban Missile Crisis.
I read the book in the mid to late 90s. I believe the cover art was a picture of a globe with a man running on top with prism like rays of light coming from where his foot touches the globe.