1. What does it mean?
암튼 is a clipped form of 아무튼. It brings a conversation back to the point, summarizes what matters despite details, or moves on from a digression.
Also written or said as amteun
2. The nuance
It can feel brisk or dismissive if it cuts off someone's concern. It is a discourse marker, not a claim that the preceding details are untrue.
3. Examples
“설명이 길어졌네. 암튼 세 시에 만나자.”
That explanation got long. Anyway, let's meet at three.
“암튼 도와준 건 정말 고마워.”
In any case, I really appreciate your help.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.