Unlikely, but review your employment contract.
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Very unlikely unless you agreed to those terms in your employment contract.
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Likely better to go ahead and have the employer review the matter prior to publishing. The general counsel's office can look at the matter and let you know up front what they think. If they disagree and say that they have ip rights in the book, then seek legal counsel before proceeding. Likely as not, with the facts that you have listed, you will get a response that they have no claim to the new book. If you have an employment contract that assigns patents, rights in creations, etc., that are typical in research and creative type positions, you would likely need to approach them regardless before publishing to get a clearance. 9 times out of 10 they will pass unless the book is specifically in your technical area of expertise. Even then, if the subject matter is not related to your employment, was written out of work, on your own time and own computer equipment/word processor, etc, then they have a tough time in proving any rigts to ownership of the manuscript. I have reviewed a similar situations for a client. Typically the employee is free to proceed with publication.