Strong Positivity in Right-Invariant Order on Braid Groups and Quasipositivity |
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Authors: | S Yu Orevkov |
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Institution: | (1) V. A. Steklov Mathematics Institute, Russian Academy of Sciences, Russia |
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Abstract: | Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
are words in
. A braid is called strongly positive if
for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. |
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Keywords: | braid right-invariant order quasipositive braid curve diagram |
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