Combinatorial manifolds are discrete analogues of smooth manifolds, constructed from simplicial complexes or well‐behaved polyhedral pieces that satisfy local topological criteria. These structures ...

Dynamical systems research on manifolds investigates the evolution of points in smooth spaces under iterative processes and flows, with diffeomorphisms serving as the central class of smooth, ...

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent. Sorting a collection of shapes is child’s play. Circles here, ...

On the left, the schematic illustration depicts the gluing rules of the Brillouin manifold, with a half-twist operation connecting the opposing faces. On the right, the BZ is divided into 64 blocks by ...

An international team of researchers has discovered that the quantum particles responsible for the vibrations of materials—which influence their stability and various other properties—can be ...