2018/04/19 by Gabriel Islambouli, Islambouli, Gabriel
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1804.06978
openalex publication_date 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to construct distinct trisections of the same genus on a fixed 4-manifold. For every k ≥ 2, we construct 2k-1 non-diffeomorphic (3k,k)-trisections on infinitely many 4-manifolds. Here, the manifolds are spun Seifert fiber spaces and the trisections come from Meier's spun trisections. The technique used to distinguish the trisections parallels an established technique for distinguishing Heegaard splittings. In particular, we show that the Nielsen classes of the generators of the fundamental group, obtained from spines of the 4-dimensional 1-handlebodies of the trisection, are isotopy invariants of the trisection. If we additionally consider the action of the automorphism group on the Nielsen classes, we obtain diffeomorphism invariants of trisections.