On bounded cohomology of amalgamated products of groups

Erovenko, Igor V.

doi:10.1155/s0161171204311142

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…. , n) satisfies conditions (10) and (11). Then, by induction on the length of a shortest word in A * n representing a braid β ∈ B n , we easily prove that the braids rel j (β) and rel j (β) coincide for each braid β ∈ B n .…”

Section: Proposition Let B N Be the Braid Group With Artinmentioning

confidence: 99%

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Pseudocharacters of braid groups and prime links

Malyutin

2010

St. Petersburg Math. J.

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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 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)| > C φ , where C φ 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.

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Section: Proposition Let B N Be the Braid Group With Artinmentioning

confidence: 99%

“…[4,5,6,9] concerning braid representations of trivial, split, and composite links.) It is well known that each pseudocharacter is conjugacy invariant (see, e.g., [10]). Consequently, we have…”

Section: Remarkmentioning

confidence: 99%

Pseudocharacters of braid groups and prime links

Malyutin

2010

St. Petersburg Math. J.

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Criteria of prime links in terms of pseudo-characters

Malyutin

2009

J Math Sci

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Pseudo-characters of groups have recently found applications in the theory of classical knots and links in R 3 . 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 if a kernel pseudo-character φ and a braid β satisfy |φ(β)| > C φ , where C φ 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 pseudocharacters from an arbitrary braid group pseudo-character that is not a homomorphism is decribed. This allows one to use an arbitrary nontrivial braid group pseudo-character for recognition of prime knots and links. Bibliography: 17 titles.

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On bounded cohomology of amalgamated products of groups

Cited by 2 publications

References 11 publications

Pseudocharacters of braid groups and prime links

Pseudocharacters of braid groups and prime links

Criteria of prime links in terms of pseudo-characters

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