Spun normal surfaces in 3-manifolds, II: The toroidal case

Ensil Kang and J. Hyam Rubinstein

Vol. 343 (2026), No. 2, 371–393

DOI: 10.2140/pjm.2026.343.371

Abstract

Spun normal surfaces are a useful way of representing proper essential surfaces using ideal triangulations for 3-manifolds with tori boundaries. Here we consider spinning surfaces in the case of a 3-manifold with a nontrivial JSJ decomposition, where each of the JSJ components is hyperbolic. We prove that a proper essential surface $\mathrm{\Sigma }$ can be spun, so long as none of the JSJ components are bundles with fiber a subsurface of $\mathrm{\Sigma }$ and the ideal triangulation satisfies similar properties to a taut structure.

Keywords

3-manifold, spun normal surface, toroidal case, ideal triangulation

Mathematical Subject Classification

Primary: 57K35

Secondary: 57K32

Milestones

Received: 16 July 2025

Revised: 29 January 2026

Accepted: 13 April 2026

Published: 22 May 2026