# Akbulut's cork involution

Akbulut's cork is the Mazur manifold $$W$$ shown in the picture below,

This manifold carries an involution of it's boundary $$f:\partial W\to \partial W$$ that exchanges a meridian of the 0-framed curve with a meridian of the dotted curve.

In Akbulut - 4-manifolds, the author says that $$f$$ is related to performing surgeries to exchange the dot with the 0-framed knot. I don't understand how this relates to $$f$$ and how $$f$$ is defined.

We can surely perform two surgeries (one along a circle and one along a 2-sphere) to get a new 4-manifold $$\tilde{W}$$ that has a Kirby diagram obtained by exchanging dot and zero in the above picture. However surgery does not affect the boundary so I do not see how this could induce a nontrivial map between the boundaries.

Precisely how is $$f$$ defined?