scholarly journals Classification of string links up to 2n-moves and link-homotopy

2021 ◽  
pp. 1-23
Author(s):  
Haruko A. Miyazawa ◽  
Kodai Wada ◽  
Akira Yasuhara
Keyword(s):  
String Links ◽  
Link Homotopy

scholarly journals Self C2-equivalence of two-component links and invariants of link maps

2018 ◽  
Vol 27 (13) ◽  
pp. 1842012
Author(s):  
Sergey A. Melikhov
Keyword(s):  
Two Component ◽  
String Links ◽  
Link Homotopy

We use Kirk’s invariant of link maps [Formula: see text] and its variations due to Koschorke and Kirk–Livingston to deduce results about classical links. Namely, we give a new proof of the Nakanishi–Ohyama classification of two-component links in [Formula: see text] up to [Formula: see text]-link homotopy. We also prove its version for string links, which is due (in a slightly different form) to Fleming–Yasuhara. The proofs do not use Clasper Theory.

scholarly journals FINITE TYPE LINK HOMOTOPY INVARIANTS

1999 ◽  
Vol 08 (06) ◽  
pp. 773-787 ◽  
Author(s):  
BLAKE MELLOR
Keyword(s):  
Finite Type ◽  
Finite Type Invariants ◽  
Chord Diagrams ◽  
Linking Numbers ◽  
String Links ◽  
Link Homotopy ◽  
Homotopy Invariants

In [2], Bar-Natan used unitrivalent diagrams to show that finite type invariants classify string links up to homotopy. In this paper, I will construct the correct spaces of chord diagrams and unitrivalent diagrams for links up to homotopy. I will use these spaces to show that, far from classifying links up to homotopy, the only rational finite type invariants of link homotopy are the linking numbers of the components.

scholarly journals The classification of links up to link-homotopy

1990 ◽  
Vol 3 (2) ◽  
pp. 389-389 ◽  
Author(s):  
Nathan Habegger ◽  
Xiao-Song Lin
Keyword(s):  
Link Homotopy

scholarly journals Homotopy classification of ribbon tubes and welded string links

2017 ◽  
pp. 713-761
Author(s):  
Benjamin Audoux ◽  
Paolo Bellingeri ◽  
Jean-Baptiste Meilhan ◽  
Emmanuel Wagner
Keyword(s):  
Homotopy Classification ◽  
String Links

scholarly journals Characterization of finite type string link invariants of degree <5

2010 ◽  
Vol 148 (3) ◽  
pp. 439-472 ◽  
Author(s):  
JEAN-BAPTISTE MEILHAN ◽  
AKIRA YASUHARA
Keyword(s):  
Finite Type ◽  
Knot Invariants ◽  
Link Invariants ◽  
Finite Type Invariants ◽  
Low Degree ◽  
String Links ◽  
Complete Set ◽  
Milnor Invariants

AbstractWe give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closures of (cabled) string links. We show that finite type invariants classify string links up toCk-moves fork≤ 5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up toCk-moves and concordance fork≤ 6.

scholarly journals Tree invariants and Milnor linking numbers with indeterminacy

2020 ◽  
Vol 29 (01) ◽  
pp. 2050002
Author(s):  
R. Komendarczyk ◽  
A. Michaelides
Keyword(s):  
Recursive Procedure ◽  
Residue Classes ◽  
Linking Numbers ◽  
String Links ◽  
Link Homotopy ◽  
Homotopy Invariants ◽  
Insight Into

This paper concerns the tree invariants of string links, introduced by Kravchenko and Polyak, which are closely related to the classical Milnor linking numbers also known as [Formula: see text]-invariants. We prove that, analogously as for [Formula: see text]-invariants, certain residue classes of tree invariants yield link-homotopy invariants of closed links. The proof is arrow diagramatic and provides a more geometric insight into the indeterminacy through certain tree stacking operations. Further, we show that the indeterminacy of tree invariants is consistent with the original Milnor’s indeterminacy. For practical purposes, we also provide a recursive procedure for computing arrow polynomials of tree invariants.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

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