2 Samuel 13:37

But Absalom fled, and went to Talmai, the son of Ammihud, king of Geshur. And David mourned for his son every day.

After ordering Amnon's death, Absalom fled to Talmai, the son of Ammihud, king of Geshur, who was his maternal grandfather. David and his servants first grieved over a false report that all the king's sons had been killed. When the surviving sons returned and showed that Amnon alone had died, David and his servants wept bitterly over him, which is the mourning described in the verse.

Absalom's flight to Geshur began his estrangement from David. David would not permit Absalom to return because he held that the murder required punishment, and that refusal increased the evils surrounding the king. While exiled and shut out from the affairs of the kingdom, Absalom turned to dangerous scheming.