Weinstein trisections of trivial surface bundles

TL;DR

This paper constructs explicit Weinstein trisections for trivial surface bundles, including a specific example for S^2×S^2, advancing understanding of symplectic 4-manifold decompositions.

Contribution

It provides the first explicit Weinstein trisection constructions for product surfaces like Σg×Σh and S^2×S^2.

Findings

Explicit Weinstein trisection of Σg×Σh constructed.

Explicit Weinstein trisection of S^2×S^2 demonstrated.

Advances understanding of symplectic 4-manifold decompositions.

Abstract

Weinstein trisection is a trisection of a symplectic 4-manifold whose 1-handlebodies are the Weinstein domain for the symplectic structure induced from an ambient manifold. Lambert-Cole, Meier, and Starkston showed that every closed symplectic 4-manifold admits a Weinstein trisection. In this paper, we construct a Weinstein trisection of $\Sigma_g\times \Sigma_h$. As a consequence of this construction, we construct a little explicit Weinstein trisection of $S^2\times S^2$.