What if your ex-wife writes a book about you and lies?

Defamation is the public (to any other people; writing a book, assuming *anyone* buys or reads it and it doesn't just sit on her computer, would qualify) making of false factual statements that damage a person's reputation or make others less likely to do business with him. (Written defamation is liable, by the way; spoken is slander.) If the ex-wife has made false factual statements, you may have a cause of action for defamation.

It's important to remember:

Opinions don't count: the ex-wife could say, "John Doe was the worst lover ever; a woman would be better off being celibate than being intimate with him," and that's just  an opinion and not actionable.

Truth is not defamation, even if harmful: if you publically claim to have been a war hero who served overseas (to use an example from some political campaigns) but in reality you were a Guard reservist who never saw deployment, that's not defamation.

However, if you believe that the ex-wife has publically made untrue negative factual statements about you, you should consult with a personal injury attorney who can evaluate the strength and economic value of your potential claim. Good luck.