Geodesic
Currents on cusped hyperbolic surfaces and denseness property
Dounnu Sasaki1 orcid
1Gakushuin University, Tokyo, Japan
Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 1077-1117

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DOI

The space GC(Σ) of geodesic currents on a hyperbolic surface Σ can be considered as a completion of the set of weighted closed geodesics on Σ when Σ is compact, since the set of rational geodesic currents on Σ, which correspond to weighted closed geodesics, is a dense subset of GC(Σ). We prove that even when Σ is a cusped hyperbolic surface with finite area, GC(Σ) has the denseness property of rational geodesic currents, which correspond not only to weighted closed geodesics on Σ but also to weighted geodesics connecting two cusps. In addition, we present an example in which a sequence of weighted closed geodesics converges to a geodesic connecting two cusps, which is an obstruction for the intersection number to extend continuously to GC(Σ). To construct the example, we use the notion of subset currents. Finally, we prove that the space of subset currents on a cusped hyperbolic surface has the denseness property of rational subset currents.
DOI : 10.4171/ggd/688
Classification : 30-XX, 20-XX
Mots-clés : geodesic current, cusped hyperbolic surface, subset current, intersection number, denseness property

Dounnu Sasaki  1

1 Gakushuin University, Tokyo, Japan 
Dounnu Sasaki. Currents on cusped hyperbolic surfaces and denseness property. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 1077-1117. doi: 10.4171/ggd/688
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     year = {2022},
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     number = {3},
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