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- Slam-dunk abstract "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. This replacement, as shown by a simple calculation, is given by coefficient n - 1/r.The inverse of the slam-dunk can be used to change any rational surgery diagram into an integer one, i.e. a surgery diagram on a framed link.".
- Slam-dunk wikiPageID "18894197".
- Slam-dunk wikiPageRevisionID "465251030".
- Slam-dunk hasPhotoCollection Slam-dunk.
- Slam-dunk subject Category:Geometric_topology.
- Slam-dunk comment "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.".
- Slam-dunk label "Slam-dunk".
- Slam-dunk sameAs m.04ych30.
- Slam-dunk sameAs Q7538547.
- Slam-dunk sameAs Q7538547.
- Slam-dunk wasDerivedFrom Slam-dunk?oldid=465251030.
- Slam-dunk isPrimaryTopicOf Slam-dunk.