Trisections of non-orientable 4-manifolds

TL;DR

This paper extends the theory of trisections to smooth, compact non-orientable 4-manifolds, establishing foundational results and diagrams analogous to the orientable case, including manifolds with boundary.

Contribution

It introduces trisections for non-orientable 4-manifolds with boundary and proves a non-orientable analogue of Laudenbach-Poénaru's theorem, enabling diagrammatic representations.

Findings

Existence of trisection diagrams for closed non-orientable 4-manifolds

Development of trisections for non-orientable 4-manifolds with boundary

Extension of classical theorems to non-orientable setting

Abstract

We study trisections of smooth, compact non-orientable 4-manifolds, and introduce trisections of non-orientable 4-manifolds with boundary. In particular, we prove a non-orientable analogue of a classical theorem of Laudenbach-Po\'enaru. As a consequence, trisection diagrams and Kirby diagrams of closed non-orientable 4-manifolds exist. We discuss how the theory of trisections may be adapted to the setting of non-orientable 4-manifolds with many examples.