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| On Reduced Lantern Relations in Mapping Class Groups? |
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Citation： |
Chaohui ZHANG.On Reduced Lantern Relations in Mapping Class Groups?[J].Chinese Annals of Mathematics B,2014,35(1):79~92 |
| Page view： 1719
Net amount： 1070 |
Authors： |
Chaohui ZHANG; |
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| 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 mapping class group of ˙S for ˙S = S\{a point}. The author
shows that the only possible relations between products of two Dehn twists and products
of mapping 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. |
Keywords： |
Dehn twists, Simple closed geodesics, Lantern relation |
Classification： |
32G15, 30F60 |
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