Kirby diagrams, trisections, and gems of PL 4-manifolds: Relationships, results, and open problems
Abstract
We review the main achievements regarding the interactions between gem theory (which makes use of edge-colored graphs to represent PL-manifolds of arbitrary dimension) and both the classical representation of PL 4-manifolds via Kirby diagrams and the more recent one via trisections. Original results also appear (in particular, about gems representing closed 4-manifolds which need 3-handles in their handle decomposition, as well as about trisection diagrams), together with open problems and further possible applications to the study of compact PL 4-manifolds.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 19–54
- Publication date
- 20 August 2026
- Language
- EN