Abstract
In 1976 Thurston associated to a 3-manifold N a marked polytope in H-1 (N; R), which measures the minimal complexity of surfaces representing homology classes and determines all fibered classes in H-1 (N; R). Recently the first and third authors associated to a presentation pi with two generators and one relator a marked polytope in H-1 (pi; R) and showed that it determines the ...
Abstract
In 1976 Thurston associated to a 3-manifold N a marked polytope in H-1 (N; R), which measures the minimal complexity of surfaces representing homology classes and determines all fibered classes in H-1 (N; R). Recently the first and third authors associated to a presentation pi with two generators and one relator a marked polytope in H-1 (pi; R) and showed that it determines the Bieri-Neumann-Strebel invariant of pi. We show that if the fundamental group of a 3-manifold N admits such a presentation pi, then the corresponding marked polytopes in H-1 (N; R) = H-1 (pi; R) agree.
Altmetric