Abstract
Let S be a hyperbolic Riemann surface with a finite area. Let G be the covering group of S acting on the hyperbolic plane H. In this paper, the author studies some algebraic relations in the map** class group of Ṡ for Ṡ = S\{a point}. The author shows that the only possible relations between products of two Dehn twists and products of map** classes determined by two parabolic elements of G are the reduced lantern relations. As a consequence, a partial solution to a problem posed by J. D. McCarthy is obtained.
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Zhang, C. On reduced lantern relations in map** class groups. Chin. Ann. Math. Ser. B 35, 79–92 (2014). https://doi.org/10.1007/s11401-013-0814-8
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DOI: https://doi.org/10.1007/s11401-013-0814-8