Zobrazeno 1 - 10
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pro vyhledávání: '"Ceniceros, Jose"'
We introduce a generalization of the quandle polynomial. We prove that our polynomial is an invariant of stuquandles. Furthermore, we use the invariant of stuquandles to define a polynomial invariant of stuck links. As a byproduct, we obtain a polyno
Externí odkaz:
http://arxiv.org/abs/2408.07695
Autor:
Ceniceros, Jose, Klivans, Max
We enhance the pointed quandle counting invariant of linkoids through the use of quivers analogously to quandle coloring quivers. This allows us to generalize the in-degree polynomial invariant of links to linkoids. Additionally, we introduce a new l
Externí odkaz:
http://arxiv.org/abs/2407.21606
Autor:
Ceniceros, Jose
This article presents an alternate way to prove a result originally proven by Harvey, Kawamuro, and Plamenvskaya in \cite{HaKaPl}. We accomplish this by explicitly constructing an overtwisted disk in the $p$-fold cyclic branched cover of $S^3$ with t
Externí odkaz:
http://arxiv.org/abs/2308.05703
We extend the quandle cocycle invariant to the context of stuck links. More precisely, we define an invariant of stuck links by assigning Boltzmann weights at both classical and stuck crossings. As an application, we define a single-variable and a tw
Externí odkaz:
http://arxiv.org/abs/2212.12605
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's entanglement while
Externí odkaz:
http://arxiv.org/abs/2207.10249
We enhance the psyquandle counting invariant for singular knots and pseudoknots using quivers analogously to quandle coloring quivers. This enables us to extend the in-degree polynomial invariants from quandle coloring quiver theory to the case of si
Externí odkaz:
http://arxiv.org/abs/2107.05668
In this short survey we review recent results dealing with algebraic structures (quandles, psyquandles, and singquandles) related to singular knot theory. We first explore the singquandles counting invariant and then consider several recent enhanceme
Externí odkaz:
http://arxiv.org/abs/2103.05620
We introduce shadow structures for singular knot theory. Precisely, we define \emph{two} invariants of singular knots and links. First, we introduce a notion of action of a singquandle on a set to define a shadow counting invariant of singular links
Externí odkaz:
http://arxiv.org/abs/2101.08775
Folded linear molecular chains are ubiquitous in biology. Folding is mediated by intra-chain interactions that "glue" two or more regions of a chain. The resulting fold topology is widely believed to be a determinant of biomolecular properties and fu
Externí odkaz:
http://arxiv.org/abs/2012.00210
We generalize the notion of the quandle polynomial to the case of singquandles. We show that the singquandle polynomial is an invariant of finite singquandles. We also construct a singular link invariant from the singquandle polynomial and show that
Externí odkaz:
http://arxiv.org/abs/2010.13295