Topological complexity is a central concept that bridges the abstract methodologies of algebraic topology with the practical challenges of robot motion planning. It provides a numerical invariant that ...

This is a preview. Log in through your library . Abstract The Lusternik-Schnirelmann category and topological complexity are important invariants of manifolds (and more generally, topological spaces).

Higher-order topological dynamics combines higher-order interactions, topology and non-linear dynamics giving rise to new emergent phenomena. These phenomena encode information which can dramatically ...