Doubly slice odd pretzel knots

The Δ-unknotting number for a knot is defined to be the minimum number of Δ-unknotting operations which deform the knot into the trivial knot. We determine the Δ-unknotting numbers for torus knots, positive pretzel knots, and positive closed 3-braids.

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Twisted Alexander polynomials of $(−2, 3, 2n+1)$-pretzel knots

Hiroshima Mathematical Journal ◽

10.32917/hmj/1583550014 ◽

2020 ◽

Vol 50 (1) ◽

pp. 43-57

Author(s):

Airi Aso

Keyword(s):

Alexander Polynomials ◽

Pretzel Knots

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CASSON-GORDON INVARIANTS OF GENUS ONE KNOTS AND CONCORDANCE TO REVERSES

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216596000382 ◽

1996 ◽

Vol 05 (05) ◽

pp. 661-677 ◽

Cited By ~ 6

Author(s):

SWATEE NAIK

Keyword(s):

Pretzel Knots ◽

Genus One

For genus one knots the Casson-Gordon invariant τ is expressed in terms of the classical signatures, generalizing an earlier result of P. Gilmer. As an application it is shown that the pretzel knots K(3, –5, 7) and K(3, –5, 17) are not concordant to their reverses.

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Pretzel knots with L-space surgeries

The Michigan Mathematical Journal ◽

10.1307/mmj/1457101813 ◽

2016 ◽

Vol 65 (1) ◽

pp. 105-130 ◽

Cited By ~ 7

Author(s):

Tye Lidman ◽

Allison H. Moore

Keyword(s):

Pretzel Knots

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On pretzel knots and Conjecture ℤ

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216516500127 ◽

2016 ◽

Vol 25 (02) ◽

pp. 1650012 ◽

Cited By ~ 1

Author(s):

Jesús Rodríguez-Viorato ◽

Francisco Gonzaléz Acuña

Keyword(s):

Equivalent Form ◽

Pretzel Knots ◽

Positive Integers

Conjecture [Formula: see text] is a knot theoretical equivalent form of the Kervaire conjecture. We show that Conjecture [Formula: see text] is true for all the pretzel knots of the form [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are odd positive integers.

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On the slice-ribbon conjecture for pretzel knots

Algebraic & Geometric Topology ◽

10.2140/agt.2015.15.2133 ◽

2015 ◽

Vol 15 (4) ◽

pp. 2133-2173 ◽

Cited By ~ 5

Author(s):

Ana G Lecuona

Keyword(s):

Pretzel Knots

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KAUFFMAN–HARARY CONJECTURE HOLDS FOR MONTESINOS KNOTS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216504003251 ◽

2004 ◽

Vol 13 (04) ◽

pp. 467-477 ◽

Cited By ~ 8

Author(s):

MARTA M. ASAEDA ◽

JÓZEF H. PRZYTYCKI ◽

ADAM S. SIKORA

Keyword(s):

Double Cover ◽

Incompressible Surfaces ◽

Pretzel Knots ◽

Prime Determinant ◽

Alternating Links

The Kauffman–Harary conjecture states that for any reduced alternating diagram K of a knot with a prime determinant p, every non-trivial Fox p-coloring of K assigns different colors to its arcs. We generalize this conjecture by stating it in terms of homology of the double cover of S3. In this way we extend the scope of the conjecture to all prime alternating links of arbitrary determinants. We first prove the Kauffman–Harary conjecture for pretzel knots and then we generalize our argument to show the generalized Kauffman–Harary conjecture for all Montesinos links. Finally, we discuss on the relation between the conjecture and Menasco's work on incompressible surfaces in exteriors of alternating links.

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