## Algebraic & Geometric Topology

### Horowitz–Randol pairs of curves in $q$–differential metrics

Anja Bankovic

#### Abstract

The Euclidean cone metrics coming from $q$–differentials on a closed surface of genus $g≥2$ 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 $q≥1$, the corresponding equivalence relation has arbitrarily large equivalence classes. In addition, we describe how these equivalence relations are related to each other.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 3107-3139.

Dates
Accepted: 31 January 2014
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513716013

Digital Object Identifier
doi:10.2140/agt.2014.14.3107

Mathematical Reviews number (MathSciNet)
MR3276858

Zentralblatt MATH identifier
1305.30019

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

#### Citation

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

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