Genus two trisections are standard

Abstract

We show that the only closed 4-manifolds admitting genus two trisections are $S^2\times S^2$ and connected sums of $S^1\times S^3$, ${\mathbb{CP}}^2$, and ${\overline{\mathbb{CP}}}^2$ with two summands. Moreover, each of these manifolds admits a unique genus two trisection up to diffeomorphism. The proof relies heavily on the combinatorics of genus two Heegaard diagrams of $S^3$. As a corollary, we classify two-component links contained in a genus two Heegaard surface for $S^3$ with a surface-sloped cosmetic Dehn surgery.

41 pages, 29 figures

References in corpus (2)

• Bridge trisections of knotted surfaces in $S^4$
• Classification of trisections and the Generalized Property R Conjecture

Cited by in corpus (19)

• Bridge trisections of knotted surfaces in $S^4$
• Classification of trisections and the Generalized Property R Conjecture
• Bridge trisections of knotted surfaces in 4--manifolds
• Simplifying indefinite fibrations on 4-manifolds
• Simplified broken Lefschetz fibrations and trisections of 4-manifolds
• Bridge trisections in ${\mathbb{CP}}^2$ and the Thom conjecture (with Corrigendum)
• Characterizing Dehn surgeries on links via trisections
• Trisections and spun 4-manifolds
• Group trisections and smooth 4-manifolds
• An Algorithm taking Kirby diagrams to Trisection diagrams
• Symplectic 4-manifolds admit Weinstein trisections
• Classifying compact 4-manifolds via generalized regular genus and G-degree
• Diagrams of *-Trisections
• Four-manifolds with shadow-complexity one
• On diagrams of simplified trisections and mapping class groups
• Right-left equivalent maps of simplified $(2,0)$-trisections with different configurations of vanishing cycles
• The genus zero, 3-component fibered links in $S^3$
• 3-manifolds lying in trisected 4-manifolds
• Vertical 3-manifolds in simplified (2, 0)-trisections of 4-manifolds