Geodesic
Characteristics of link primeness in terms of pseudo-characters
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 150-161

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Pseudo-characters of Artin's braid groups and properties of links represented by braids are studied. The notion of kernel pseudo-character is introduced. It is proved that if a kernel pseudo-character $\phi$ and a braid $\beta$ satisfy $|\phi(\beta)|>C_\phi$, where $C_\phi$ is the defect of $\phi$, then $\beta$ represents a prime (i.e., noncomposite, nonsplit, and nontrivial) link. A method for obtaining nontrivial kernel pseudo-characters from an arbitrary nontrivial braid group pseudo-character is described. Bibl. – 17 titles. 
@article{ZNSL_2008_353_a14,
     author = {A. V. Malyutin},
     title = {Characteristics of link primeness in terms of pseudo-characters},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--161},
     publisher = {mathdoc},
     volume = {353},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a14/}
}
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A. V. Malyutin. Characteristics of link primeness in terms of pseudo-characters. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 150-161. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a14/