Classification of trisections and the Generalized Property R Conjecture

Abstract

We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisections of the four-sphere. As an application, we prove a stable version of the Generalized Property R Conjecture for $c$-component links with tunnel number at most $c$.

arXiv comment14 pages, 2 figures. This paper subsumes the results of arXiv:1503.08511

References in corpus (4)

• Heegaard splittings of compact 3-manifolds
• Genus two trisections are standard
• Waldhausen's Theorem
• A classification of automorphisms of compact 3-manifolds

Cited by in corpus (21)

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• Bridge trisections of knotted surfaces in 4--manifolds
• Genus two trisections are standard
• Knot traces and concordance
• Calculating the homology and intersection form of a 4-manifold from a trisection diagram
• Isotopies of surfaces in 4-manifolds via banded unlink diagrams
• Trisections of surface complements and the Price twist
• Doubly pointed trisection diagrams and surgery on 2-knots
• Characterizing Dehn surgeries on links via trisections
• Trisections of 3-manifold bundles over $S^1$
• Group trisections and smooth 4-manifolds
• Symplectic 4-manifolds admit Weinstein trisections
• Filling braided links with trisected surfaces
• Comparing 4-Manifolds in the Pants Complex via Trisections
• Trisections and Ozsvath-Szabo cobordism invariants
• Thin Position through the lens of trisections of 4-manifolds
• Minimal genus four manifolds
• Efficient multisections of odd-dimensional tori
• Band diagrams of immersed surfaces in 4-manifolds
• Bridge trisections and Seifert solids
• Infinitely many standard trisection diagrams for Gluck twisting