The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL $4$-manifolds with empty or connected boundary, called semi-simple and weak semi-simple crystallizations, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the regular genus, the Gurau degree, the gem-complexity and the (gem-induced) trisection genus. The main theorem, yielding a summarizing result on the topic, is an original contribution. Moreover, in the present paper the additivity of regular genus with respect to connected sum is proved to hold for all compact $4$-manifolds with empty or connected boundary which admit weak semi-simple crystallizations.

Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants / Casali, Maria Rita; Cristofori, Paola; Gagliardi, Carlo. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 52:(2020), pp. 1-28. [10.13137/2464-8728/30760]

Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants

Maria Rita Casali;Paola Cristofori;Carlo Gagliardi
2020

Abstract

The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL $4$-manifolds with empty or connected boundary, called semi-simple and weak semi-simple crystallizations, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the regular genus, the Gurau degree, the gem-complexity and the (gem-induced) trisection genus. The main theorem, yielding a summarizing result on the topic, is an original contribution. Moreover, in the present paper the additivity of regular genus with respect to connected sum is proved to hold for all compact $4$-manifolds with empty or connected boundary which admit weak semi-simple crystallizations.
2020
52
1
28
Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants / Casali, Maria Rita; Cristofori, Paola; Gagliardi, Carlo. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 52:(2020), pp. 1-28. [10.13137/2464-8728/30760]
Casali, Maria Rita; Cristofori, Paola; Gagliardi, Carlo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1204202
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