2025/05/11 by Rafiqi, Ahmad
#05A05 #37B40 #37E30 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2505.06930
We present a simple method to compute the Teichmüller polynomial of the fibered face of a hyperbolic 3-manifold Mϕ obtained as the mapping torus of a pseudo-Anosov homeomorphism ϕ of a closed surface. We assume ϕ has orientable invariant foliations and fixes each singular trajectory. We use a characterisation of such homeomorphisms in terms of a permutation of a finite set of integers to give a direct implementation of McMullens algorithm using train tracks. Train tracks with a single vertex suffice in this case. As an application, for each p∈ℤ≥0, we find an infinite sequence of Teichmüller polynomials Θg,p associated to pseudo-Anosov maps on surfaces of genus g≥2, such that the hyperbolic 3-manifold obtained as the mapping torus has first Betti number g. These polynomials realize a positive proportion of bi-Perron units of each degree as pseudo-Anosov stretch-factors.