Estimating trisection genus via gem theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| 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 |