On independence of some pseudocharacters on braid groups

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...

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Bibliographic Details
Published in:St. Petersburg mathematical journal 2013-12, Vol.24 (6), p.863-876
Main Authors: Dynnikov, I. A., Shastin, V. A.
Format: Article
Language:English
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Summary: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 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.
ISSN:1061-0022
1547-7371
DOI:10.1090/S1061-0022-2013-01270-2