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.

A Possible Infinite Number of Components in a Single Crystalline Phase: On the Isomorphism of Brivaracetam–Guest Molecules

2018 ◽  
Vol 18 (9) ◽  
pp. 4807-4810 ◽  
Author(s):  
Nicolas Couvrat ◽  
Morgane Sanselme ◽  
Yohann Cartigny ◽  
Frederic De Smet ◽  
Sandrine Rome ◽  
...  
Keyword(s):  
Infinite Number ◽  
Crystalline Phase ◽  
Guest Molecules ◽  
Single Crystalline ◽  
Number Of Components

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 Minimally Supported Frequency (MSF) d-Dilation Wavelets

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1284
Author(s):  
Aparna Vyas ◽  
Gibak Kim
Keyword(s):  
Infinite Number ◽  
Geometric Construction ◽  
The Other ◽  
Wavelet Sets ◽  
Number Of Components ◽  
Wavelet Set

In this paper, we provide a geometric construction of a symmetric 2n-interval minimally supported frequency (MSF) d-dilation wavelet set with d∈(1,∞) and characterize all symmetric d-dilation wavelet sets. We also provide two special kinds of symmetric d-dilation wavelet sets, one of which has 4m-intervals whereas the other has (4m+2)-intervals, for m∈N. In addition, we construct a family of d-dilation wavelet sets that has an infinite number of components.

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