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# statementaboutThe word problem inbraidgroups

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Hi,

i have read a statement from Sossinsky and Prasolov' s book "Knots, Lİnks, Braids and 3-Manifold", it says that two reduced word represent isotopic braids if and only if they have the same reduced form, page 54. My claim is that this statement is not true: take $b_2b_1b_2^{-1}b_3^{-1}b_3^{-1}$ and $b_3^{-1}b_2b_3b_2b_1b_2^{-1}b_2^{-1}b_3{-1}b_2^{-1}$. b_3^{-1}b_2b_3b_2b_1b_2^{-1}b_2^{-1}b_3^{-1}b_2^{-1}\$. They represent isotopic braids but they are not the same. What is the correction of this statement?

zati

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# statement about word problem

Hi,

i have read a statement from Sossinsky and Prasolov' s book "Knots, Lİnks, Braids and 3-Manifold", it says that two reduced word represent isotopic braids if and only if they have the same reduced form, page 54. My claim is that this statement is not true: take $b_2b_1b_2^{-1}b_3^{-1}b_3^{-1}$ and $b_3^{-1}b_2b_3b_2b_1b_2^{-1}b_2^{-1}b_3{-1}b_2^{-1}$. They represent isotopic braids but they are not the same. What is the correction of this statement?

zati
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