Compact 4-manifolds admitting special handle decompositions (Q2037028)

The origin of the problem of this article is the following problem posed by Kirby -- does every simply-connected closed PL 4-manifold have a special handlebody decomposition, i.e., a handlebody decomposition without 1- and 3-handles? In this article, the authors detect a class of compact simply-connected PL 4-manifolds with empty or connected boundary, which admit such decompositions and, therefore, can be represented by (undotted) framed links. Moreover, this class includes any compact simply-connected PL 4-manifold with empty or connected boundary having colored triangulations that minimize the combinatorially defined PL invariants regular genus, gem-complexity or \(G\)-degree among all such manifolds with the same second Betti number.