Timeline for Kirby diagram of the complement of a subhandlebody of a smooth closed 4-manifold

7 events

when toggle format	what		by	license	comment
Dec 2 at 23:17	vote	accept	blancket
Dec 2 at 18:14	history	became hot network question
Dec 2 at 16:10	answer	added	Marco Golla		timeline score: 7
Dec 2 at 16:04	comment	added	Ryan Budney		There is a general prescription for this when the handle structures come from a Morse function on $X$ (which you then restrict to the submanifold, and to the exterior of the submanifold, respectively). The prescription looks much like the Wirthinger presentation.
Dec 2 at 15:47	comment	added	Ryan Budney		In your first question presumably you meant to say "a Kirby diagram" not "the" diagram. Handle structures on the complement of submanifolds is an old topic, in dimension 3 the standard is the one that generates the Wirthinger presentation of knot complements. You can do the same kind of construction in 4-manifolds but I suspect the level of detail in the resulting handle decomposition is heavily dependent on how precise your original (manifold, submanifold) pair is described.
Dec 2 at 10:32	history	edited	HJRW	CC BY-SA 4.0	Corrected typo in title.
Dec 2 at 10:14	history	asked	blancket	CC BY-SA 4.0