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math.GT2025
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…
math.GT2025
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 .…
math.GT2025
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…