Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 5 (2014), 3107-3139.
Horowitz–Randol pairs of curves in $q$–differential metrics
The Euclidean cone metrics coming from –differentials on a closed surface of genus define an equivalence relation on homotopy classes of closed curves, where two classes are equivalent if they have the equal length in every such metric. We prove an analogue of the result of Randol for hyperbolic metrics (building on the work of Horowitz): for every integer , the corresponding equivalence relation has arbitrarily large equivalence classes. In addition, we describe how these equivalence relations are related to each other.
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 3107-3139.
Received: 19 January 2014
Accepted: 31 January 2014
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Bankovic, Anja. Horowitz–Randol pairs of curves in $q$–differential metrics. Algebr. Geom. Topol. 14 (2014), no. 5, 3107--3139. doi:10.2140/agt.2014.14.3107. https://projecteuclid.org/euclid.agt/1513716013