15 citations · 84 across the 28 of their papers we have counts for
28 papers · 1 filter
Around the Andreadakis-Johnson filtration
Yusuke Kuno
The Andreadakis-Johnson filtration and its associated construction, known as the Johnson homomorphism, are useful tools in group theory. They provide a step-by-step approach to stu…
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…
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…
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…
A note on Penner's cocycle on the fatgraph complex
Yusuke Kuno, Kae Takezawa
We study a 1-cocycle on the fatgraph complex of a punctured surface introduced by Penner. We present an explicit cobounding cochain for this cocycle, whose formula involves a summa…
Generalized Dehn twists in low-dimensional topology
Yusuke Kuno, Gwenael Massuyeau, Shunsuke Tsuji
The generalized Dehn twist along a closed curve in an oriented surface is an algebraic construction which involves intersections of loops in the surface. It is defined as an automo…