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Compact 4-manifolds admitting special handle decompositions

2021; Springer Science+Business Media; Volume: 115; Issue: 3 Linguagem: Inglês

10.1007/s13398-021-01001-x

1579-1505

María Rita Casali, Paola Cristofori,

Topological and Geometric Data Analysis

In this paper we study colored triangulations of compact PL 4-manifolds with empty or connected boundary which induce handle decompositions lacking in 1-handles or in 1- and 3-handles, thus facing also the problem, posed by Kirby, of the existence of special handle decompositions for any simply-connected closed PL 4-manifold. In particular, we 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.