Unit surface-framed surgery realizes a Dehn twist
= Unit surface-framed surgery realizes a Dehn twist
{title2=$\mu\mapsto\mu\pm\lambda$}
Put a simple closed curve in a surface collar and use its <surface framing>. Filling its deleted tubular neighborhood along $\mu\pm\lambda$ inserts one full positive or negative twist of the annulus between the collar levels. Thus surgery of coefficient $\pm1$ changes the gluing by a <Dehn twist> or its inverse. The exact sign depends on the orientations of the seam and normal direction.