Combinatorial growth in the modular group

  • Ara Basmajian

    CUNY, New York, USA
  • Robert Suzzi Valli

    Manhattan College, Riverdale, NY, USA
Combinatorial growth in the modular group cover
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Abstract

We consider an exhaustion of the modular orbifold by compact subsurfaces and show that the growth rate, in terms of word length, of the reciprocal geodesics on such subsurfaces (so named low lying reciprocal geodesics) converges to the growth rate of the full set of reciprocal geodesics on the modular orbifold. We derive a similar result for the low lying geodesics and their growth rate convergence to the growth rate of the full set of closed geodesics

Cite this article

Ara Basmajian, Robert Suzzi Valli, Combinatorial growth in the modular group. Groups Geom. Dyn. 16 (2022), no. 2, pp. 683–703

DOI 10.4171/GGD/667