3 papers
math.GT2025
On the 2-loop part of the Johnson cokernel
Yusuke Kuno, Masatoshi Sato
We study stable Sp-decompositions of the cokernel of the Johnson homomorphism. Continuing the work of Conant in 2016, which identified the 1-loop part of the Johnson cokernel as th…
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
Emergent version of Drinfeld's associator equations
Yusuke Kuno
The works of Alekseev and Torossian [AT] and Alekseev, Enriquez, and Torossian [AET] show that any solution of Drinfeld's associator equations gives rise to a solution of the Kashi…