Slam-dunk
In mathematics, particularly low-dimensional topology, the
slam-dunk is a particular modification of a given surgery diagram in the 3-sphere for a 3-manifold. The name, but not the move, is due to Tim Cochran. Let
K be a component of the link in the diagram and
J be a component that circles
K as a meridian. Suppose
K has integer coefficient
n and
J has coefficient a rational number
r. Then we can obtain a new diagram by deleting
J and changing the coefficient of
K to
n-1/r. This is the slam-dunk. The name of the move is suggested by the proof that these diagrams give the same 3-manifold. First, do the surgery on
K, replacing a tubular neighborhood of
K by another solid torus
T according to the surgery coefficient
n. Since
J is a meridian, it can be pushed, or "slam dunked", into
T. Since
n is an integer,
J intersects the meridian of
T once, and so
J must be isotopic to a longitude of
T. Thus when we now do surgery on
J, we can think of it as replacing
T by another solid torus.