2017/03/16 by Nickolas A. Castro, Castro, Nickolas A.
Computer Science · Mathematics · #57M99 #Advanced Algebra and Logic #Advanced Graph Theory Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1703.05846
openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We extend the theory of relative trisections of smooth, compact, oriented 4-manifolds with connected boundary given by Gay and Kirby to include 4-manifolds with an arbitrary number of boundary components. Additionally, we provide sufficient conditions under which relatively trisected 4-manifolds can be glued to one another along diffeomorphic boundary components so as to induce a trisected manifold. These two results allow us to define a category \textrmTri whose objects are smooth, closed, oriented 3-manifolds equipped with open book decompositions, and morphisms are relatively trisected cobordisms. Additionally, we extend the Hopf stabilization of open book decompositions to a relative stabilization of relative trisections.