Kirby diagrams, trisections and gems of PL 4-manifolds: relationships, results and open problems

Maria Rita Casali; Paola Cristofori

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arXiv · 2502.01757

Kirby diagrams, trisections and gems of PL 4-manifolds: relationships, results and open problems

Maria Rita Casali·Paola Cristofori

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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.

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Maria Rita Casali, Paola Cristofori. 2025-02-03. Kirby diagrams, trisections and gems of PL 4-manifolds: relationships, results and open problems. https://arxiv.org/abs/2502.01757

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