Criteria of prime links in terms of pseudo-characters

Standard

Criteria of prime links in terms of pseudo-characters. / Malyutin, A. V.

In: Journal of Mathematical Sciences , Vol. 161, No. 3, 01.07.2009, p. 437-442.

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

Author

Malyutin, A. V. / Criteria of prime links in terms of pseudo-characters. In: Journal of Mathematical Sciences . 2009 ; Vol. 161, No. 3. pp. 437-442.

BibTeX

@article{6cbd78fb51d2489e91daa847db140ae5,

title = "Criteria of prime links in terms of pseudo-characters",

abstract = "Pseudo-characters of groups have recently found applications in the theory of classical knots and links in ℝ3. More precisely, there is a connection between pseudo-characters of Artin's braid groups and properties of links represented by braids. In the present work, this connection is investigated and the notion of kernel pseudo-characters of braid groups is introduced. It is proved that a kernel pseudo-character 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 pseudo-characters is studied and a way to obtain nontrivial kernel pseudo-characters from an arbitrary braid group pseudo-character that is not a homomorphisrn is described. This allows one to use an arbitrary nontrivial braid group pseudo-character for recognition of prime knots and links. Bibliography: 17 titles.",

author = "Malyutin, {A. V.}",

year = "2009",

month = jul,

day = "1",

doi = "10.1007/s10958-009-9572-2",

language = "русский",

volume = "161",

pages = "437--442",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Criteria of prime links in terms of pseudo-characters

AU - Malyutin, A. V.

PY - 2009/7/1

Y1 - 2009/7/1

N2 - Pseudo-characters of groups have recently found applications in the theory of classical knots and links in ℝ3. More precisely, there is a connection between pseudo-characters of Artin's braid groups and properties of links represented by braids. In the present work, this connection is investigated and the notion of kernel pseudo-characters of braid groups is introduced. It is proved that a kernel pseudo-character 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 pseudo-characters is studied and a way to obtain nontrivial kernel pseudo-characters from an arbitrary braid group pseudo-character that is not a homomorphisrn is described. This allows one to use an arbitrary nontrivial braid group pseudo-character for recognition of prime knots and links. Bibliography: 17 titles.

AB - Pseudo-characters of groups have recently found applications in the theory of classical knots and links in ℝ3. More precisely, there is a connection between pseudo-characters of Artin's braid groups and properties of links represented by braids. In the present work, this connection is investigated and the notion of kernel pseudo-characters of braid groups is introduced. It is proved that a kernel pseudo-character 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 pseudo-characters is studied and a way to obtain nontrivial kernel pseudo-characters from an arbitrary braid group pseudo-character that is not a homomorphisrn is described. This allows one to use an arbitrary nontrivial braid group pseudo-character for recognition of prime knots and links. Bibliography: 17 titles.

UR - http://www.scopus.com/inward/record.url?scp=70449524644&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9572-2

DO - 10.1007/s10958-009-9572-2

M3 - статья

AN - SCOPUS:70449524644

VL - 161

SP - 437

EP - 442

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 47487492