On independence of some pseudocharacters on braid groups

Dynnikov, I.; Shastin, V.

doi:10.1090/S1061-0022-2013-01270-2

On independence of some pseudocharacters on braid groups
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by I. A. Dynnikov and V. A. Shastin
Translated by: A. Plotkin

St. Petersburg Math. J. 24 (2013), 863-876

DOI: https://doi.org/10.1090/S1061-0022-2013-01270-2

Published electronically: September 23, 2013

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Abstract:

It is proved that the pseudocharacter defined on the braid group by the signature of braid closures is linearly independent of all pseudocharacters obtained from the twist number via the Malyutin operators, provided that the number of strands is greater than 4. This pseudocharacter is shown to have a nontrivial kernel part. It is observed that the operators $I$ and $R$ defined by Malyutin on the space of pseudocharacters satisfy the Heisenberg relation, and that some of Malyutin’s results are standard consequences of this fact.

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