Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Criteria of prime links in terms of pseudo-characters. / Malyutin, A. V.
в: Journal of Mathematical Sciences , Том 161, № 3, 01.07.2009, стр. 437-442.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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