Can I travel outside the U.S. after I receive my permanent residency?

You can apply for a reentry permit (on form I-131) before you leave the US. You can depart before the reentry permit is approved.

With such a reentry permit, you can return to the US even after one year until the reentry permit’s expiration date. Reentry permits are issued for two years at a time, however, you cannot renew a reentry permit while abroad. You can return to the US for a short time and apply for a new one, but subsequent reentry permits may only be approved for one year at a time.