Pseudocharacters of braid groups and prime links

Author:
A. V. Malyutin

Translated by:
the author

Original publication:
Algebra i Analiz, tom **21** (2009), nomer 2.

Journal:
St. Petersburg Math. J. **21** (2010), 245-259

MSC (2000):
Primary 20F36

DOI:
https://doi.org/10.1090/S1061-0022-10-01093-9

Published electronically:
January 21, 2010

MathSciNet review:
2549454

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Abstract | References | Similar Articles | Additional Information

Abstract: *Pseudocharacters* of groups have recently found an application in the theory of classical knots and links in . More precisely, there is a relationship between pseudocharacters of Artin's braid groups and the properties of links represented by braids. In the paper, this relationship is investigated and the notion of *kernel* pseudocharacters of braid groups is introduced. It is proved that if a kernel pseudocharacter and a braid satisfy , where is the *defect* of , then represents a prime link (i.e., a link that is noncomposite, nonsplit, and nontrivial). Furthermore, the space of braid group pseudocharacters is studied and a way is described to obtain nontrivial kernel pseudocharacters from an arbitrary braid group pseudocharacter that is not a homomorphism. This makes it possible to employ an arbitrary nontrivial braid group pseudocharacter for the recognition of prime knots and links.

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Additional Information

**A. V. Malyutin**

Affiliation:
St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Email:
malyutin@pdmi.ras.ru

DOI:
https://doi.org/10.1090/S1061-0022-10-01093-9

Keywords:
Knot,
link,
braid,
pseudocharacter,
quasimorphism

Received by editor(s):
September 16, 2008

Published electronically:
January 21, 2010

Additional Notes:
Supported in part by RFBR (grant 08-01-00379a) and the RF President Program for Support of leading Scientific Schools (grant NSh-2460.2008.1112)

Article copyright:
© Copyright 2010
American Mathematical Society