The verb abnegate means to deny or renounce something. Scientists abnegate the existence of little green spacemen from Mars.
The verb abnegate also means to surrender a position of power. If you serve on too many committees, you may need to cut back. You could abnegate the treasurer position for P.T.A., in order to have more time to serve as president of Band Boosters. What's the difference between abnegate and abdicate? Both mean to renounce power or authority, but abdicate is usually reserved for higher offices of power. The king abdicates the throne. The CEO, who gives up day-to-day responsibility? He abnegates responsibility.