Essential tori in 3-manifolds not detected in any characteristic

2024/11/24 by Grace S. Garden, Garden, Grace S., Benjamin Martin +3
Computer Science · Mathematics · #57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2411.15680

openalex publication_date 2024/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Infinite families of 3-dimensional closed graph manifolds and closed Seifert fibered spaces are exhibited, each member of which contains an essential torus not detected by ideal points of the variety of SL₂(\mathbbF)-characters over any algebraically closed field \mathbbF.

Related

• Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds
• Representation varieties detect essential surfaces
• An invitation to Culler-Shalen theory in arbitrary characteristic
• An algorithm to find vertical tori in small Seifert fiber spaces
• Limiting characters at ideal points detecting twice-punctured tori