Estimating trisection genus via gem theory

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Casali, Maria Rita, Cristofori, Paola
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910905122422784
author Casali, Maria Rita
Cristofori, Paola
author_facet Casali, Maria Rita
Cristofori, Paola
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_04434
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Estimating trisection genus via gem theory
Casali, Maria Rita
Cristofori, Paola
Geometric Topology
57Q15 - 57K40 - 57M15
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.
title Estimating trisection genus via gem theory
topic Geometric Topology
57Q15 - 57K40 - 57M15
url https://arxiv.org/abs/2504.04434