66 citations · 276 across the 61 of their papers we have counts for
63 papers
Surface Braid Invariants from Yang-Baxter Operators and Their Cohomology
Masahico Saito, Emanuele Zappala
Surface braids are a generalization of braids to surfaces in the 4-disk. They are described by planar graphs called charts, and sequences of braid words called braid systems, that…
Quantum Cocycle Invariants of Knots from Yang-Baxter Cohomology
Masahico Saito, Emanuele Zappala
Yang-Baxter operators (YBOs) have been employed to construct quantum knot invariants. More recently, cohomology theories for YBOs have been independently developed, drawing inspira…
Planar Equivalence of Knotoids and Quandle Invariants
Mohamed Elhamdadi, Wout Moltmaker, Masahico Saito
While knotoids on the sphere are well-understood by a variety of invariants, knotoids on the plane have proven more subtle to classify due to their multitude over knotoids on the s…
Deformation Cohomology for Braided Commutativity
Masahico Saito, Emanuele Zappala
Braided algebras are algebraic structures consisting of an algebra endowed with a Yang-Baxter operator, satisfying some compatibility conditions.Yang-Baxter Hochschild cohomology w…
Yang-Baxter Solutions from Categorical Augmented Racks
Masahico Saito, Emanuele Zappala
An augmented rack is a set with a self-distributive binary operation induced by a group action, and has been extensively used in knot theory. Solutions to the Yang-Baxter equation…
Betti Numbers of Prodsimplicial Complexes for Directed Graphs with Applications to Word Reductions
Lina Fajardo Gómez, Margherita Maria Ferrari, Nataša Jonoska +1
We propose custom made cell complexes, in particular prodsimplicial complexes, in order to analyze data consisting of directed graphs. These are constructed by attaching cells that…