Diagrams of *-Trisections

Abstract

In this note, we provide a generalization for the definition of a trisection of a 4-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by finding a trisection-theoretic way to perform logarithmic surgery. In addition, we describe how to perform 1-surgery on closed trisections. The insight gained from this description leads us to the classification of an infinite family of genus three trisections. We include an appendix where we extend two classic results for relative trisections for the case when the trisection surface is closed.

arXiv commentThe definitions are carefully study in Sections 3 and 4. Comments are welcome

References in corpus (7)

• Bridge trisections of knotted surfaces in $S^4$
• Bridge trisections of knotted surfaces in 4--manifolds
• Genus two trisections are standard
• Trisections of 4-manifolds with Boundary
• Calculating the homology and intersection form of a 4-manifold from a trisection diagram
• Torsions and intersection forms of 4-manifolds from trisection diagrams
• Trisecting Smooth 4-dimensional Cobordisms

Cited by in corpus (1)

• Trisections and Ozsvath-Szabo cobordism invariants