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Pseudocharacters of braid groups and prime links. / Malyutin, A. V.

In: St. Petersburg Mathematical Journal, Vol. 21, No. 2, 01.12.2010, p. 245-259.

Research output: Contribution to journal › Article › peer-review

Harvard

Malyutin, AV 2010, 'Pseudocharacters of braid groups and prime links', St. Petersburg Mathematical Journal, vol. 21, no. 2, pp. 245-259. https://doi.org/10.1090/S1061-0022-10-01093-9

APA

Malyutin, A. V. (2010). Pseudocharacters of braid groups and prime links. St. Petersburg Mathematical Journal, 21(2), 245-259. https://doi.org/10.1090/S1061-0022-10-01093-9

Vancouver

Malyutin AV. Pseudocharacters of braid groups and prime links. St. Petersburg Mathematical Journal. 2010 Dec 1;21(2):245-259. https://doi.org/10.1090/S1061-0022-10-01093-9

Author

Malyutin, A. V. / Pseudocharacters of braid groups and prime links. In: St. Petersburg Mathematical Journal. 2010 ; Vol. 21, No. 2. pp. 245-259.

BibTeX

@article{72012fb2c59440e6a9c027ef665cf16b,
title = "Pseudocharacters of braid groups and prime links",
abstract = "Pseudocharacters of groups have recently found an application in the theory of classical knots and links in R3. 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 φ and a braid β satisfy |φ(β)| > Cφ, where Cφ is the defect of φ, then β 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.",
keywords = "Braid, Knot, Link, Pseudocharacter, Quasimorphism",
author = "Malyutin, {A. V.}",
year = "2010",
month = dec,
day = "1",
doi = "10.1090/S1061-0022-10-01093-9",
language = "русский",
volume = "21",
pages = "245--259",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - Pseudocharacters of braid groups and prime links

AU - Malyutin, A. V.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Pseudocharacters of groups have recently found an application in the theory of classical knots and links in R3. 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 φ and a braid β satisfy |φ(β)| > Cφ, where Cφ is the defect of φ, then β 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.

AB - Pseudocharacters of groups have recently found an application in the theory of classical knots and links in R3. 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 φ and a braid β satisfy |φ(β)| > Cφ, where Cφ is the defect of φ, then β 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.

KW - Braid

KW - Knot

KW - Link

KW - Pseudocharacter

KW - Quasimorphism

UR - http://www.scopus.com/inward/record.url?scp=84871346090&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-10-01093-9

DO - 10.1090/S1061-0022-10-01093-9

M3 - статья

AN - SCOPUS:84871346090

VL - 21

SP - 245

EP - 259

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 47487598