Horowitz–Randol pairs of curves in q–differential metrics

Bankovic, Anja

doi:10.2140/agt.2014.14.3107

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

Anja Bankovic

Algebraic & Geometric Topology 14 (2014) 3107–3139

DOI: 10.2140/agt.2014.14.3107

Abstract

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

Keywords

compact surfaces, flat metrics, hyperbolic metrics

Mathematical Subject Classification 2010

Primary: 57M50

References

Publication

Received: 19 January 2014

Accepted: 31 January 2014

Published: 5 November 2014

Authors

Anja Bankovic
Department of Mathematics Boston College Carney Hall Chestnut Hill, MA 02467-3806 USA
https://www2.bc.edu/anja-bankovic/

Volume 14, issue 5 (2014)