2015/11/20 by Arpan Kabiraj, Kabiraj, Arpan
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1511.06563
openalex publication_date 2015/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pair of distinct free homotopy classes of closed curves in an orientable surface F with negative Euler characteristic is said to be length equivalent if for any hyperbolic structure on F, the length of the geodesic representative of one class is equal to the length of the geodesic representative of the other class. Suppose α and β are two intersecting oriented closed curves on F and P and Q are any two intersection points between them. If the two terms ⟨α*Pβ⟩ and ⟨α*Qβ⟩ in [⟨α⟩,⟨β⟩], the Goldman bracket between them, are the same, then we construct infinitely many pairs of length equivalent curves in F. These pairs correspond to the terms of the Goldman bracket between a power of α and β. As a special case, our construction shows that given a self-intersecting geodesic α of F and any self-intersection point P of α, we get a sequence of such pairs. Furthermore if α is a filling curve then these pairs are also filling.