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Cavicchioli, Alberto; Spaggiari, Fulvia, (2021)  - On reduced complexity of closed piecewise linear 5-manifolds  - PERIODICA MATHEMATICA HUNGARICA, Articolo su rivista - Articolo in rivista (262) (, , ) - pagg. 1 - 15

Abstract: The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed 5-manifolds up to piecewise-linear (PL) homeomorphism. For this, we use the combinatorial approach to the topology of PL manifolds by means of a special kind of edge-colored graphs, called crystallizations. Within this representation theory, Bracho and Montejano introduced in 1987 a nonnegative numerical invariant, called the reduced complexity, for any closed n-dimensional PL manifold. Here we obtain the complete classification of all closed connected smooth 5-manifolds of reduced complexity less than or equal to 20. In particular, this gives a combinatorial characterization of S2×S3 among closed connected spin PL 5-manifolds.