2025/04/06 by María Rita Casali, Casali, Maria Rita, Paola Cristofori +1
Computer Science · Mathematics · #57Q15 - 57K40 - 57M15 #Advanced Operator Algebra Research #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2504.04434
openalex publication_date 2025/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gems are a particular type of edge-colored graphs, dual to colored triangulations, which represent compact PL-manifolds of arbitrary dimension, both in the closed and boundary case. In the present paper, gem theory is used to approach trisections of PL 4-manifolds, so as to prove that: - the graph-defined invariant regular genus is an upper bound for the trisection genus of each closed 4-manifold; - a trisection diagram can be directly obtained from any gem of a closed 4-manifold. Moreover, suitable extensions of the above results are presented for compact 4-manifolds with connected boundary.