Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Patrick D. Shanahan"'
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87766be03f738f55c770d83a7d9c90b4
http://arxiv.org/abs/2010.05009
http://arxiv.org/abs/2010.05009
Autor:
Jim Hoste, Patrick D. Shanahan
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8314e95c7f9d6622c490c95be410f2b0
http://arxiv.org/abs/1707.01519
http://arxiv.org/abs/1707.01519
Autor:
Jim Hoste, Patrick D. Shanahan
Publikováno v:
Algebr. Geom. Topol. 17, no. 5 (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.
16 pages, 4 f
16 pages, 4 f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61fcc2e1c689024454915aa99328f5a4
https://projecteuclid.org/euclid.agt/1510841483
https://projecteuclid.org/euclid.agt/1510841483
Publikováno v:
Journal of Knot Theory and Its Ramifications. 28:1950060
A partial order on prime knots can be defined by declaring [Formula: see text], if there exists an epimorphism from the knot group of [Formula: see text] onto the knot group of [Formula: see text]. Suppose that [Formula: see text] is a 2-bridge knot
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::362aaa788a147505c3d2a69ded532795
https://doi.org/10.1142/s0218216519500603
https://doi.org/10.1142/s0218216519500603
Autor:
Dennis G. Zill, Patrick D. Shanahan
Complex Analysis: A First Course with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with c
Autor:
Jim Hoste, Patrick D. Shanahan
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88f79bd15d7267b622850b61fb8ae9d8
Publikováno v:
Mathematics Magazine. 83:83-99
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing e...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::68c938c22676fdcd8f10f9d9c518888f
https://doi.org/10.4169/002557010x482853
https://doi.org/10.4169/002557010x482853
Autor:
Jim Hoste, Patrick D. Shanahan
Publikováno v:
Mathematics of Computation. 76:1521-1546
We describe an algorithm for computing boundary slopes of 2-bridge links. As an example, we work out the slopes of the links obtained by 1/k surgery on one component of the Borromean rings. A table of all boundary slopes of all 2-bridge links with 10
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b1d0b2e3a999bdeeea2f97b3926a41ed
https://doi.org/10.1090/s0025-5718-07-01936-9
https://doi.org/10.1090/s0025-5718-07-01936-9
Autor:
Jim Hoste, Patrick D. Shanahan
Publikováno v:
Journal of Knot Theory and Its Ramifications. 13:193-209
The fundamental group of a 2-bridge knot has a particularly nice presentation, having only two generators and a single relation. For certain families of 2-bridge knots, such as the torus knots, or the twist knots, the relation takes on an especially
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fa28402cb37bf4765f73cfe4bb20b32f
https://doi.org/10.1142/s0218216504003081
https://doi.org/10.1142/s0218216504003081
Autor:
Jim Hoste, Patrick D. Shanahan
Publikováno v:
Journal of Knot Theory and Its Ramifications. 10:625-639
In this paper we compute the trace field for the family of hyperbolic twist knots. We describe this field as a simple extension ℚ(z0) where z0 is a specified root of a particular irreducible polynemial Φn(z)∈ℤ[z]. As a consequence, we find tha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ccb42da169fa0e59a2b07c50b5dc492
https://doi.org/10.1142/s0218216501001049
https://doi.org/10.1142/s0218216501001049