17 citations
- University of South AlabamaUS10 papers
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- California Institute of TechnologyUS1 paper
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12 papers · 1 filter
Frobenius Modules and Essential Surface Cobordisms
J. Scott Carter, Masahico Saito
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential…
Symmetric Extensions of Dihedral Quandles and Triple Points of Non-orientable Surfaces
J. Scott Carter, Kanako Oshiro, Masahico Saito
Quandles with involutions that satisfy certain conditions, called good involutions, can be used to color non-orientable surface-knots. We use subgroups of signed permutation matric…
Cocycle Deformations of Algebraic Identities and R-matrices
J. Scott Carter, Alissa Crans, Mohamed Elhamdadi +1
For an arbitrary identity L=R between compositions of maps L and R on tensors of vector spaces V, a general construction of a 2-cocycle condition is given. These 2-cocycles corresp…
Polynomial cocycles of Alexander quandles and applications
Kheira Ameur, Masahico Saito
Cocycles are constructed by polynomial expressions for Alexander quandles. As applications, non-triviality of some quandle homology groups are proved, and quandle cocycle invariant…
Tangle embeddings and quandle cocycle invariants
Kheira Ameur, Mohamed Elhamdadi, Tom Rose +2
To study embeddings of tangles in knots, we use quandle cocycle invariants. Computations are carried out for the tables of knots and tangles, to investigate which tangles may or ma…
Virtual Knot Invariants from Group Biquandles and Their Cocycles
J. Scott Carter, Mohamed Elhamdadi, Masahico Saito +2
A group-theoretical method, via Wada's representations, is presented to distinguish Kishino's virtual knot from the unknot. Biquandles are constructed for any group using Wada's br…