The study of periodic orbits in three-dimensional (3D) dynamics remains a challenging frontier. While braid group theory has successfully been used to study orbit structures on surfaces, its classical form falls short in three dimensions.
WEB3
Backed by the Marie Skłodowska-Curie Actions programme, the project, 'Welded braids on 3D dynamics' (WEB3) , will use welded braid groups, a 3D analogue of classical braids to study 3D dynamics. Specifically, it aims to develop new mathematical tools to analyse the behaviour of periodic points in 3D manifolds, thereby extending the understanding of topological dynamics beyond current limits.
New pathways
By bridging braid group theory with low-dimensional topology, WEB3 promises to open new pathways in the study of dynamical systems, fostering innovation and expanding the mathematical framework used to explore 3D orbit structures.