The goal of this paper is to give some theorems which relate tothe problem of classifying smooth 4{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 reducedcomplexity, for any closed n{dimensional PL manifold. Here we obtain the complete classification of all closed connected smooth 4-manifolds of reduced complexity less than or equal to 14.
CLASSIFYING COMBINATORIAL 4-MANIFOLDS UP TO COMPLEXITY / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: BOLETÍN DE LA SOCIEDAD MATEMÁTICA MEXICANA. - ISSN 1405-213X. - STAMPA. - 14 (3):(2008), pp. 303-319.
CLASSIFYING COMBINATORIAL 4-MANIFOLDS UP TO COMPLEXITY
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2008
Abstract
The goal of this paper is to give some theorems which relate tothe problem of classifying smooth 4{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 reducedcomplexity, for any closed n{dimensional PL manifold. Here we obtain the complete classification of all closed connected smooth 4-manifolds of reduced complexity less than or equal to 14.
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