Zobrazeno 1 - 10
of 76
pro vyhledávání: '"CRANS, ALISSA S."'
We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, the classes tOS and tOSn correspond to finitary compositions of trivial
Externí odkaz:
http://arxiv.org/abs/2004.10227
Autor:
Horvat, Eva, Crans, Alissa S.
Publikováno v:
Journal of Knot Theory and Its Ramifications, Vol. 29, No. 02, 2040008 (2020)
We investigate the relationship between the quandle and biquandle coloring invariant and obtain an enhancement of the quandle and biquandle coloring invariants using biquandle structures. We also continue the study of biquandle homomorphisms into a m
Externí odkaz:
http://arxiv.org/abs/1907.10259
We continue the study of the quandle of homomorphisms into a medial quandle begun in Crans and Nelson. We show that it suffices to consider only medial source quandles, and therefore the structure theorem of Jedlicka et al. provides a characterizatio
Externí odkaz:
http://arxiv.org/abs/1808.01738
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
Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and their relati
Externí odkaz:
http://arxiv.org/abs/1603.08590
Autor:
Crans, Alissa S., Wagemann, Friedrich
We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the relation between
Externí odkaz:
http://arxiv.org/abs/1310.4705
Autor:
Crans, Alissa S., Nelson, Sam
If $A$ is an abelian quandle and $Q$ is a quandle, the hom set $\mathrm{Hom}(Q,A)$ of quandle homomorphisms from $Q$ to $A$ has a natural quandle structure. We exploit this fact to enhance the quandle counting invariant, providing an example of links
Externí odkaz:
http://arxiv.org/abs/1310.0852
Publikováno v:
Fundamenta Mathematicae 225 (2014) pp. 75-94
The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homolog
Externí odkaz:
http://arxiv.org/abs/1306.1506
Publikováno v:
In Journal of Pure and Applied Algebra November 2019 223(11):5017-5029
