2 papers
math.GT2026
The nontrivial kernel of Manturov-Nikonov map from classical braids to virtual braids
Yangzhou Liu
In 2022, V. O. Manturov and I. M. Nikonov \cite{Man22} constructed two composite maps, one of them is following: $$PB_{n+1} \overset{p_k}{\rightarrow} CPB_{n} \overset{f_d}{\righta…
math.GT2026
Secant-quandle: an invariant of braids and knots
Seongjeong Kim, Yangzhou Liu, Vassily Olegovich Manturov
We construct a novel invariant of braids and knots, called the secant-quandle (SQ), derived from homotopy classes of generic secants and generic horizontal trisecants. This invaria…