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MR2327038 (2008i:20048) 20F36 (37E30 57M07 58D05)
Crisp, John; Wiest, Bert Quasi-isometrically embedded subgroups of braid and diffeomorphism groups. Trans. Amer. Math. Soc. 359 (2007), no. 11, 5485–5503.
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