scholarly journals Towards invariants of surfaces in $4$-space via classical link invariants

2008 ◽  
Vol 361 (01) ◽  
pp. 237-265 ◽  
Author(s):  
Sang Youl Lee
Keyword(s):  
Link Invariants ◽  
Classical Link

CLASSICAL LINK INVARIANTS AND THE HAWAIIAN EARRINGS SPACE

1992 ◽  
Vol 01 (04) ◽  
pp. 327-342
Author(s):  
TIM D. COCHRAN
Keyword(s):  
Infinite Number ◽  
Number Of Components ◽  
Link Invariants ◽  
Classical Link

We show that, in search of link invariants more discriminating than Milnor's [Formula: see text]-invariants, one is naturally led to consider seemingly pathological objects such as links with an infinite number of components and the join of an infinite number of circles (Hawaiian earrings space). We define an infinite homology boundary link, and show that any finite sublink of an infinite homology boundary link has vanishing Milnor's invariants. Moreover, all links known to have vanishing Milnor's invariants are finite sublinks of infinite homology boundary links. We show that the exterior of an infinite homology boundary link admits a map to the Hawaiian earrings space, and that this may be employed to get a factorization of K. E. Orr's omega-invariant through a rather simple space.

scholarly journals DEALTERNATING NUMBERS AND CLASSICAL LINK INVARIANTS

2012 ◽  
Vol 28 (1) ◽  
pp. 93-99
Author(s):  
Myung-Jae Kim ◽  
Dong-Hee Lee ◽  
Dong-Seok Kim
Keyword(s):  
Link Invariants ◽  
Classical Link

IDEAL COSET INVARIANTS FOR SURFACE-LINKS IN ℝ4

2013 ◽  
Vol 22 (09) ◽  
pp. 1350052 ◽  
Author(s):  
YEWON JOUNG ◽  
JIEON KIM ◽  
SANG YOUL LEE
Keyword(s):  
Normal Form ◽  
Polynomial Ring ◽  
Gröbner Basis ◽  
Quotient Ring ◽  
Grobner Basis ◽  
Link Invariant ◽  
Link Invariants ◽  
Classical Link ◽  
Marked Graph

In [Towards invariants of surfaces in 4-space via classical link invariants, Trans. Amer. Math. Soc.361 (2009) 237–265], Lee defined a polynomial [[D]] for marked graph diagrams D of surface-links in 4-space by using a state-sum model involving a given classical link invariant. In this paper, we deal with some obstructions to obtain an invariant for surface-links represented by marked graph diagrams D by using the polynomial [[D]] and introduce an ideal coset invariant for surface-links, which is defined to be the coset of the polynomial [[D]] in a quotient ring of a certain polynomial ring modulo some ideal and represented by a unique normal form, i.e. a unique representative for the coset of [[D]] that can be calculated from [[D]] with the help of a Gröbner basis package on computer.

scholarly journals Classical link invariants from the framizations of the Iwahori–Hecke algebra and the Temperley–Lieb algebra of type A

2017 ◽  
Vol 26 (09) ◽  
pp. 1743005 ◽  
Author(s):  
D. Goundaroulis ◽  
S. Lambropoulou
Keyword(s):  
Hecke Algebras ◽  
Jones Polynomial ◽  
Hecke Algebra ◽  
Type A ◽  
Link Invariants ◽  
Classical Link

In this paper, we first present the construction of the new 2-variable classical link invariants arising from the Yokonuma–Hecke algebras [Formula: see text], which are not topologically equivalent to the Homflypt polynomial. We then present the algebra [Formula: see text] which is the appropriate Temperley–Lieb analogue of [Formula: see text], as well as the related 1-variable classical link invariants, which in turn are not topologically equivalent to the Jones polynomial. Finally, we present the algebra of braids and ties which is related to the Yokonuma–Hecke algebra, and also its quotient, the partition Temperley–Lieb algebra [Formula: see text] and we prove an isomorphism of this algebra with a subalgebra of [Formula: see text].

scholarly journals Applying Lipson's state models to marked graph diagrams of surface-links

2015 ◽  
Vol 24 (10) ◽  
pp. 1540003 ◽  
Author(s):  
Yewon Joung ◽  
Seiichi Kamada ◽  
Sang Youl Lee
Keyword(s):  
Link Invariant ◽  
Link Invariants ◽  
Classical Link ◽  
Marked Graph ◽  
Kauffman Polynomial ◽  
State Models

A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial F(a, u). In this paper, we apply Lipson's state models to marked graph diagrams of surface-links, and observe when they induce surface-link invariants.

Multivariate Alexander quandles, II. The involutory medial quandle of a link

2020 ◽  
Vol 29 (05) ◽  
pp. 2050024 ◽  
Author(s):  
Lorenzo Traldi
Keyword(s):  
Link Invariants ◽  
Classical Link

Joyce showed that for a classical knot [Formula: see text], the order of the involutory medial quandle is [Formula: see text]. Generalizing Joyce’s result, we show that for a classical link [Formula: see text] of [Formula: see text] components, the order of the involutory medial quandle is [Formula: see text]. In particular, [Formula: see text] is infinite if and only if [Formula: see text]. We also relate [Formula: see text] to several other link invariants.

scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG
Keyword(s):  
The Other ◽  
Polynomial Invariant ◽  
Link Invariants ◽  
Fusion Categories ◽  
New Family ◽  
Kauffman Polynomial ◽  
Twist Structure

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

Sign in / Sign up

Export Citation Format

Share Document