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On independence of some pseudocharacters on braid groups


Authors: I. A. Dynnikov and V. A. Shastin
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 24 (2012), nomer 6.
Journal: St. Petersburg Math. J. 24 (2013), 863-876
MSC (2010): Primary 20F36
Published electronically: September 23, 2013
MathSciNet review: 3097552
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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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Additional Information

I. A. Dynnikov
Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences, Gubkin str. 8, Moscow 119991, Russia
Email: dynnikov@mech.math.msu.su

V. A. Shastin
Affiliation: Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia
Email: shast.fds@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-2013-01270-2
Keywords: Braid group, pseudocharacter, twist numbers, signature
Received by editor(s): December 24, 2011
Published electronically: September 23, 2013
Additional Notes: Supported by RFBR (grant no. 10-01-91056-NCNI) and by the Government of RF (grant no. 2010-220-01-077)
Article copyright: © Copyright 2013 American Mathematical Society