Abstract
Pseudocharacters of groups have recently found an application in the theory of classical knots and links in R 3 . More precisely, there is a relationship between pseudocharacters of Artin's braid groups and the properties of links repre- sented 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)| >C φ ,w hereCφ is the defect of φ ,t henβ 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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