Geodesic
ON POWERS OF HALF-TWISTS IN M(0, 2n)
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 333-338

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DOI

We use elementary skein theory to prove a version of a result of Stylianakis (Stylianakis, The normal closure of a power of a half-twist has infinite index in the mapping class group of a punctured sphere, arXiv:1511.02912) who showed that under mild restrictions on m and n, the normal closure of the mth power of a half-twist has infinite index in the mapping class group of a sphere with 2n punctures. 
MASBAUM, GREGOR. ON POWERS OF HALF-TWISTS IN M(0, 2n). Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 333-338. doi: 10.1017/S0017089517000143
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