The present paper studies the relationship between handle-decompositions of PL 4-manifolds and the so called "crystallization theory", which represents PL n-manifolds by means of pseudosimplicial triangulations admitting exactly n+1 vertices. Within this theory, the combinatorial invariant "regular genus" plays a central role. In particular, the authors obtain the characterization of PL 4-manifolds $M^4$ (with empty or connected boundary $\partial M^4$) satisfying suitable conditions concerning the regular genus $G(M^4)$, the rank of the fundamental group $rk(\pi_1(M^4))$, and the boundary regular genus $G(\partial M^4)$. As a consequence, it is completed the classification of PL 4-manifolds with (possibly disconnected) boundary up to regular genus two.

Handle-decompositions of PL 4-manifolds / Casali, Maria Rita; L., Malagoli. - In: CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES. - ISSN 1245-530X. - STAMPA. - 38:(1997), pp. 141-160.

### Handle-decompositions of PL 4-manifolds

#### Abstract

The present paper studies the relationship between handle-decompositions of PL 4-manifolds and the so called "crystallization theory", which represents PL n-manifolds by means of pseudosimplicial triangulations admitting exactly n+1 vertices. Within this theory, the combinatorial invariant "regular genus" plays a central role. In particular, the authors obtain the characterization of PL 4-manifolds $M^4$ (with empty or connected boundary $\partial M^4$) satisfying suitable conditions concerning the regular genus $G(M^4)$, the rank of the fundamental group $rk(\pi_1(M^4))$, and the boundary regular genus $G(\partial M^4)$. As a consequence, it is completed the classification of PL 4-manifolds with (possibly disconnected) boundary up to regular genus two.
##### Scheda breve Scheda completa Scheda completa (DC)
38
141
160
Handle-decompositions of PL 4-manifolds / Casali, Maria Rita; L., Malagoli. - In: CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES. - ISSN 1245-530X. - STAMPA. - 38:(1997), pp. 141-160.
Casali, Maria Rita; L., Malagoli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/450754
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