Zobrazeno 1 - 10
of 250
pro vyhledávání: '"Saito, Masahico"'
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 sphere and a lack of invariants that detect a diagram's planar nature.
Externí odkaz:
http://arxiv.org/abs/2407.07489
Autor:
Saito, Masahico, Zappala, Emanuele
Braided algebras are algebraic structures consisting of an algebra endowed with a Yang-Baxter operator, satisfying some compatibility conditions. Yang-Baxter Hochschild cohomology was introduced by the authors to classify infinitesimal deformations o
Externí odkaz:
http://arxiv.org/abs/2407.02663
Autor:
Saito, Masahico, Zappala, Emanuele
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 (YBE) have been also used for knots, since the discovery of the Jones
Externí odkaz:
http://arxiv.org/abs/2312.01033
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 are products of simplices and are suited to study data of acyclic dir
Externí odkaz:
http://arxiv.org/abs/2305.05818
Autor:
Saito, Masahico, Zappala, Emanuele
Braided algebras are associative algebras endowed with a Yang-Baxter operator that satisfies certain compatibility conditions involving the multiplication. Along with Hochschild cohomology of algebras, there is also a notion of Yang-Baxter cohomology
Externí odkaz:
http://arxiv.org/abs/2305.04173
Autor:
Saito, Masahico, Zappala, Emanuele
A rack is a set with a binary operation that is right-invertible and self-distributive, properties diagrammatically corresponding to Reidemeister moves II and III, respectively. A rack is said to be an {\it augmented rack} if the operation is written
Externí odkaz:
http://arxiv.org/abs/2207.04570
Autor:
Saito, Masahico, Zappala, Emanuele
We introduce the notion of fundamental heap for compact orientable surfaces with boundary embedded in $3$-space, which is an isotopy invariant of the embedding. It is a group, endowed with a ternary heap operation, defined using diagrams of surfaces
Externí odkaz:
http://arxiv.org/abs/2109.07569
Autor:
Saito, Masahico, Zappala, Emanuele
A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a group with t
Externí odkaz:
http://arxiv.org/abs/2102.09593
Autor:
Saito, Masahico, Zappala, Emanuele
A heap is a set with a certain ternary operation that is self-distributive (TSD) and exemplified by a group with the operation $(x,y,z)\mapsto xy^{-1}z$. We introduce and investigate framed link invariants using heaps. In analogy with the knot group,
Externí odkaz:
http://arxiv.org/abs/2011.03684
We introduce skein theoretic techniques to compute the Yang-Baxter (YB) homology and cohomology groups of the R-matrix corresponding to the Jones polynomial. More specifically, we show that the YB operator $R$ for Jones, normalized for homology, admi
Externí odkaz:
http://arxiv.org/abs/2004.00691