COEXISTENCE OF COILED SURFACES AND SPANNING SURFACES FOR KNOTS AND LINKS

It is a well-known procedure for constructing a torus knot or link that first we prepare an unknotted torus and meridian disks in its complementary solid tori, and second we smooth the intersections of the boundaries of the meridian disks uniformly. Then we obtain a torus knot or link on the unknotted torus and its Seifert surface made of meridian disks. In the present paper, we generalize this procedure by using a closed fake surface and show that the two resulting surfaces obtained by smoothing triple points uniformly are essential. We also show that a knot obtained by this procedure satisfies the Neuwirth conjecture and that the distance of two boundary slopes for the knot is equal to the number of triple points of the closed fake surface.

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Identifying non-pseudo-alternating knots by using the free factor property of minimal genus Seifert surfaces

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216521500723 ◽

2021 ◽

Author(s):

Keisuke Himeno ◽

Masakazu Teragaito

Keyword(s):

Seifert Surface ◽

Major Difficulty ◽

Flat Surfaces ◽

Minimal Genus ◽

Pretzel Knots ◽

Seifert Surfaces ◽

Manifold Theory ◽

Knots And Links

Pseudo-alternating knots and links are defined constructively via their Seifert surfaces. By performing Murasugi sums of primitive flat surfaces, such a knot or link is obtained as the boundary of the resulting surface. Conversely, it is hard to determine whether a given knot or link is pseudo-alternating or not. A major difficulty is the lack of criteria to recognize whether a given Seifert surface is decomposable as a Murasugi sum. In this paper, we propose a new idea to identify non-pseudo-alternating knots. Combining with the uniqueness of minimal genus Seifert surface obtained through sutured manifold theory, we demonstrate that two infinite classes of pretzel knots are not pseudo-alternating.

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Flat plumbing basket and contact structure

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216521500103 ◽

2021 ◽

Vol 30 (02) ◽

pp. 2150010

Author(s):

Tetsuya Ito ◽

Keiji Tagami

Keyword(s):

Lower Bounds ◽

Contact Structure ◽

Seifert Surface ◽

Open Book ◽

Open Book Decomposition ◽

Knots And Links ◽

Torus Links

A flat plumbing basket is a Seifert surface consisting of a disk and bands contained in distinct pages of the disk open book decomposition of the 3-sphere. In this paper, we examine close connections between flat plumbing baskets and the contact structure supported by the open book. As an application we give lower bounds for the flat plumbing basket numbers and determine the flat plumbing basket numbers for various knots and links, including the torus links.

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TEM Studies of Grain Boundary Films in Si3N4 Ceramics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100088968 ◽

1991 ◽

Vol 49 ◽

pp. 930-931

Author(s):

H.-J. Kleebe ◽

J.S. Vetrano ◽

J. Bruley ◽

M. Rühle

Keyword(s):

Mechanical Properties ◽

High Temperature ◽

Silicon Nitride ◽

Hot Isostatic Pressing ◽

Amorphous Film ◽

Liquid Phase Sintering ◽

Second Phase ◽

High Temperature Mechanical Properties ◽

Triple Points ◽

Boundary Films

It is expected that silicon nitride based ceramics will be used as high-temperature structural components. Though much progress has been made in both processing techniques and microstructural control, the mechanical properties required have not yet been achieved. It is thought that the high-temperature mechanical properties of Si3N4 are limited largely by the secondary glassy phases present at triple points. These are due to various oxide additives used to promote liquid-phase sintering. Therefore, many attempts have been performed to crystallize these second phase glassy pockets in order to improve high temperature properties. In addition to the glassy or crystallized second phases at triple points a thin amorphous film exists at two-grain junctions. This thin film is found even in silicon nitride formed by hot isostatic pressing (HIPing) without additives. It has been proposed by Clarke that an amorphous film can exist at two-grain junctions with an equilibrium thickness.

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Knots and Links

10.1017/cbo9780511809767 ◽

2004 ◽

Cited By ~ 99

Author(s):

Peter R. Cromwell

Keyword(s):

Knots And Links

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On independence of iterated Whitehead doubles in the knot concordance group

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216518500037 ◽

2018 ◽

Vol 27 (01) ◽

pp. 1850003

Author(s):

Kyungbae Park

Keyword(s):

Correction Term ◽

Khovanov Homology ◽

Floer Theory ◽

Knot Concordance ◽

Torus Knot ◽

Linearly Independent ◽

Heegaard Floer

Let [Formula: see text] be the positively clasped untwisted Whitehead double of a knot [Formula: see text], and [Formula: see text] be the [Formula: see text] torus knot. We show that [Formula: see text] and [Formula: see text] are linearly independent in the smooth knot concordance group [Formula: see text] for each [Formula: see text]. Further, [Formula: see text] and [Formula: see text] generate a [Formula: see text] summand in the subgroup of [Formula: see text] generated by topologically slice knots. We use the concordance invariant [Formula: see text] of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the [Formula: see text]-invariant of knot Floer theory and the [Formula: see text]-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of [Formula: see text] for any [Formula: see text] generalizing a result for [Formula: see text] of Hedden, Kim and Livingston.

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