Sutured manifolds and L²-Betti numbers

2018/04/25 by Gerrit Herrmann, Herrmann, Gerrit
Computer Science · Mathematics · #57M27 #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.1804.09519

openalex publication_date 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the virtual fibering theorem of Agol we show that a sutured 3-manifold (M, R₊,R_-,γ) is taut if and only if the ℓ²-Betti numbers of the pair (M,R_-) are zero. As an application we can characterize Thurston norm minimizing surfaces in a 3-manifold N with empty or toroidal boundary by the vanishing of certain ℓ²-Betti numbers.

Related

• The sutured Thurston norm
• The virtual fibering theorem for 3-manifolds
• Universal L²-torsion and sutured decomposition for 3-manifolds
• Taut sutured manifolds and twisted homology
• On Thurston's Euler class one conjecture