Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Shanahan, Patrick D."'
We investigate the nonorientable 4-genus $\gamma_4$ of a special family of 2-bridge knots, the twist knots and double twist knots $C(m,n)$. Because the nonorientable 4-genus is bounded by the nonorientable 3-genus, it is known that $\gamma_4(C(m,n))
Externí odkaz:
http://arxiv.org/abs/2208.07850
We consider the relationship between the crosscap number $\gamma$ of knots and a partial order on the set of all prime knots, which is defined as follows. For two knots $K$ and $J$, we say $K \geq J$ if there exists an epimorphism $f:\pi_1(S^3-K) \lo
Externí odkaz:
http://arxiv.org/abs/2010.05009
A partial order on prime knots can be defined by declaring $J\ge K$ if there exists an epimorphism from the knot group of $J$ onto the knot group of $K$. Suppose that $J$ is a 2-bridge knot that is strictly greater than $m$ distinct, nontrivial knots
Externí odkaz:
http://arxiv.org/abs/1810.05146
Publikováno v:
Journal of Knot Theory and its Ramifications, vol. 28, no. 3, 2019
We compute Cayley graphs and automorphism groups for all finite $n$-quandles of two-bridge and torus knots and links, as well as torus links with an axis.
Comment: 16 pages; version 2 is the final version to appear in Journal of Knot Theory and
Comment: 16 pages; version 2 is the final version to appear in Journal of Knot Theory and
Externí odkaz:
http://arxiv.org/abs/1806.05727
Autor:
Hoste, Jim, Shanahan, Patrick D.
Given a presentation for a rack $\mathcal R$, we define a process which systematically enumerates the elements of $\mathcal R$. The process is modeled on the systematic enumeration of cosets first given by Todd and Coxeter. This generalizes and impro
Externí odkaz:
http://arxiv.org/abs/1707.01519
Autor:
Hoste, Jim, Shanahan, Patrick D.
Publikováno v:
Algebr. Geom. Topol. 17 (2017) 2807-2823
We prove a conjecture of Przytycki which asserts that the $n$-quandle of a link $L$ in the 3-sphere is finite if and only if the fundamental group of the $n$-fold cyclic branched cover of the 3-sphere, branched over $L$, is finite.
Comment: 16 p
Comment: 16 p
Externí odkaz:
http://arxiv.org/abs/1606.08324
Autor:
Hoste, Jim, Shanahan, Patrick D.
In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe som
Externí odkaz:
http://arxiv.org/abs/1602.01852
Autor:
Hoste, Jim, Shanahan, Patrick D.
We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, we derive formulae for these twisted Alexander pol
Externí odkaz:
http://arxiv.org/abs/1206.1894
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound
Externí odkaz:
http://arxiv.org/abs/1007.3278
Autor:
Hoste, Jim, Shanahan, Patrick D.
Publikováno v:
Algebr. Geom. Topol. 10 (2010) 1221-1244
In this article we study a partial ordering on knots in the 3-sphere where K_1 is greater than or equal to K_2 if there is an epimorphism from the knot group of K_1 onto the knot group of K_2 which preserves peripheral structure. If K_1 is a 2-bridge
Externí odkaz:
http://arxiv.org/abs/1002.1106