Non-conjugate braids with the same closure link from density of representations

Stoimenow, A.

doi:10.1016/j.matpur.2010.08.003

Cited by 4 publications

(5 citation statements)

References 28 publications

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“…It is a consequence of Theorem 1.1 that any composite knot K of braid index b(K) 4 has infinitely many nonconjugate minimal braid representatives. (This insight was also obtained in [22]. )…”

Section: §5 Tablesupporting

confidence: 64%

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Exchange Moves and Nonconjugate Braid Representatives of Knots

Shinjo¹,

Stoimenow²

2019

Nagoya Math. J.

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Section: §5 Tablesupporting

confidence: 64%

“…Our result can be seen, for knots, as such a general construction. It is also a precursor to a follow-up paper [20], where we discuss in more detail the case of links (for which also special cases were known [21,22]), and extend our main result. §2.…”

Section: §1 Overviewmentioning

confidence: 77%

Exchange Moves and Nonconjugate Braid Representatives of Knots

Shinjo¹,

Stoimenow²

2019

Nagoya Math. J.

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“…Since we proved in [25] that is dense in a unitary group for proper even on some subgroups of , it also follows that is irreducible on , and that thus, for as we already argued, is a scalar matrix.…”

Section: On the Burau Kernel And Imagementioning

confidence: 61%

“…Since from (2.11), which is more than the components of , we have that is not such a torus link. Then has infinitely many conjugacy classes of (reducible, and hence exchangeable) -braid representatives by [25].…”

Section: Application To Linksmentioning

confidence: 99%

Subsymmetric exchanged braids and the Burau matrix

Stoimenow

2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We develop a method based on the Burau matrix to detect conditions on the linking numbers of braid strands. Our main application is to iterated exchanged braids. Unless the braid permutation fixes both braid edge strands, we establish under some fairly generic conditions on the linking numbers a ‘subsymmetry’ property; in particular at most two such braids can be mutually conjugate. As an addition, we prove that the Burau kernel is contained in the commutator subgroup of the pure braid group. We discuss also some properties of the Burau image.

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“…This question was studied in [SS,Sh,St1,St2] where it was shown that under some additional and technical assumptions, iterations of exchange moves indeed produce infinitely many nonconjugate braids.…”

Section: Tetsuya Itomentioning

confidence: 99%