Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants
Abstract
The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL -manifolds with empty or connected boundary, called {\it semi-simple} and {\it weak semi-simple crystallizations}, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the {\it regular genus}, the {\it Gurau degree}, the {\it gem-complexity} and the {\it (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 -manifolds with empty or connected boundary which admit weak semi-simple crystallizations.
Cite
@article{arxiv.2004.07894,
title = {Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants},
author = {Maria Rita Casali and Paola Cristofori and Carlo Gagliardi},
journal= {arXiv preprint arXiv:2004.07894},
year = {2021}
}
Comments
21 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1910.08777