Pseudo-trisections of four-manifolds with boundary

Shintaro Fushida-Hardy

doi:10.4153/s0008414x25000069

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arXiv · 2401.09599

Pseudo-trisections of four-manifolds with boundary

Shintaro Fushida-Hardy

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Abstract

We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove existence and uniqueness of pseudo-trisections, and further establish a one-to-one correspondence between pseudo-trisections and their diagrammatic representations. We next introduce the concept of pseudo-bridge trisections of neatly embedded surfaces in smooth oriented compact 4-manifolds. We develop a diagrammatic theory of pseudo-bridge trisections and provide examples of computations of invariants of neatly embedded surfaces in 4-manifolds using said diagrams.

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Shintaro Fushida-Hardy. 2024-01-17. Pseudo-trisections of four-manifolds with boundary. https://doi.org/10.4153/s0008414x25000069

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