scholarly journals Eigenvalue varieties of Brunnian links

2017 ◽  
Vol 17 (4) ◽  
pp. 2039-2050
Author(s):  
François Malabre
Keyword(s):  
Brunnian Links

scholarly journals Homotopy Brunnian links and the $\kappa $-invariant

2014 ◽  
Vol 143 (3) ◽  
pp. 1347-1362 ◽  
Author(s):  
F. R. Cohen ◽  
R. Komendarczyk ◽  
C. Shonkwiler
Keyword(s):  
Brunnian Links

scholarly journals On surgery along Brunnian links in 3–manifolds

2006 ◽  
Vol 6 (5) ◽  
pp. 2417-2453 ◽  
Author(s):  
Jean-Baptiste Meilhan
Keyword(s):  
Brunnian Links

scholarly journals Brunnian links, claspers and Goussarov–Vassiliev finite type invariants

2007 ◽  
Vol 142 (3) ◽  
pp. 459-468 ◽  
Author(s):  
KAZUO HABIRO
Keyword(s):  
Finite Type ◽  
Finite Type Invariants ◽  
Type Invariant ◽  
Brunnian Links

AbstractGoussarov and the author independently proved that two knots in S3 have the same values of finite type invariants of degree <n if and only if they are Cn-equivalent, which means that they are equivalent up to modification by a kind of geometric commutator of class n. This property does not generalize to links with more than one component.In this paper, we study the case of Brunnian links, which are links whose proper sublinks are trivial. We prove that if n ≥ 1, then an (n+1)-component Brunnian link L is Cn-equivalent to an unlink. We also prove that if n ≥ 2, then L can not be distinguished from an unlink by any Goussarov–Vassiliev finite type invariant of degree <2n.

A FAMILY OF BRUNNIAN LINKS BASED ON EDWARDS' CONSTRUCTION OF VENN DIAGRAMS

2001 ◽  
Vol 10 (01) ◽  
pp. 97-107 ◽  
Author(s):  
ARNAUD MAES ◽  
CORINNE CERF
Keyword(s):  
Infinite Family ◽  
Venn Diagrams ◽  
The Family ◽  
Brunnian Links

We construct an infinite family of brunnian links whose projections give the family of Venn diagrams for many sets constructed by Edwards.

scholarly journals FOUR OBSERVATIONS ON n-TRIVIALITY AND BRUNNIAN LINKS

2000 ◽  
Vol 09 (02) ◽  
pp. 213-219 ◽  
Author(s):  
Theodore B. Stanford
Keyword(s):  
Knot Theory ◽  
Recent Innovation ◽  
Long Time ◽  
The Relationship ◽  
Brunnian Links

Brunnian links have been known for a long time in knot theory, whereas the idea of n-triviality is a recent innovation. We illustrate the relationship between the two concepts with four short theorems.

scholarly journals FINITE TYPE INVARIANTS AND MILNOR INVARIANTS FOR BRUNNIAN LINKS

2008 ◽  
Vol 19 (06) ◽  
pp. 747-766 ◽  
Author(s):  
KAZUO HABIRO ◽  
JEAN-BAPTISTE MEILHAN
Keyword(s):  
Quadratic Form ◽  
Finite Type ◽  
Finite Type Invariants ◽  
Type Invariant ◽  
Milnor Invariants ◽  
Link Homotopy ◽  
Homotopy Invariants ◽  
Brunnian Links

A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, Habiro proved that the restriction to Brunnian links of any Goussarov–Vassiliev finite type invariant of (n + 1)-component links of degree < 2n is trivial. The purpose of this paper is to study the first nontrivial case. We show that the restriction of an invariant of degree 2n to (n + 1)-component Brunnian links can be expressed as a quadratic form on the Milnor link-homotopy invariants of length n + 1.

POLYNOMIALS FOR A FAMILY OF BRUNNIAN LINKS

2000 ◽  
Vol 09 (05) ◽  
pp. 587-609 ◽  
Author(s):  
TAT-HUNG CHAN
Keyword(s):  
Closed Form ◽  
Recurrence Relations ◽  
Jones Polynomials ◽  
Homfly Polynomials ◽  
Brunnian Links

We apply skein relations to derive recurrence relations for the HOMFLY polynomials of a family of Brunnian links. Solution of the recurrence relations yields closed-form formulas for the HOMFLY and hence the Jones polynomials.

Generalized Brunnian links

1969 ◽  
Vol 36 (1) ◽  
pp. 31-32 ◽  
Author(s):  
David E. Penney
Keyword(s):  
Brunnian Links

scholarly journals New criteria and constructions of brunnian links

2020 ◽  
pp. 2043008
Author(s):  
Sheng Bai ◽  
Weibiao Wang
Keyword(s):  
General Procedure ◽  
New Criteria ◽  
Brunnian Links

We present two practical and widely applicable methods, including some criteria and a general procedure, for detecting Brunnian property of a link, if each component is known to be unknot. The methods are based on observation and handwork. They are used successfully for all Brunnian links known so far. Typical examples and extensive experiments illustrate their efficiency. As an application, infinite families of Brunnian links are created and we establish a general way to construct new ones in bulk.

scholarly journals Brunnian links are determined by their complements

2001 ◽  
Vol 1 (1) ◽  
pp. 143-152 ◽  
Author(s):  
Brian S Mangum ◽  
Theodore Stanford
Keyword(s):  
Brunnian Links
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