6 papers
Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence
Ayaka Shimizu, Yoshiro Yaguchi
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surfac…
The crossing matrix and the extended first Johnson homomorphism of a braid group
Yusuke Kuno, Yoshiro Yaguchi
We compare two crossed homomorphisms on a braid group, one defined diagrammatically and the other defined algebraically. We show that these crossed homomorphisms are essentially th…
The CN matrix of a pure braid projection
Yuko Ozawa, Ayaka Shimizu, Yoshiro Yaguchi
The CN matrix of an -braid projection is an matrix such that each entry indicates the number of crossings between and strands of .…
Characterization of the OU matrix of a braid diagram
Ayaka Shimizu, Yoshiro Yaguchi
The OU matrix of a braid diagram is a square matrix that represents the number of over/under crossings of each pair of strands. In this paper, the OU matrix of a pure braid diagram…
Orbits by the up-down action of braid diagrams
Komal Negi, Ayaka Shimizu, Yoshiro Yaguchi +1
The set of all virtual or classical braid diagrams forms a monoid and gives a natural monoid action on a direct product of called the up-down action. In this paper, w…
Determinant of the OU matrix of a braid diagram
Ayaka Shimizu, Yoshiro Yaguchi
In this paper, we define the OU matrix of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the deter…