Magnetic helicity is a fundamental quantity of magnetohydrodynamics that carries
topological information about the magnetic field. By 'topological information', we usually refer …

We construct and explore two-band topological semimetals in different spatial dimensions
that are protected by unstable homotopies. Dubbed “delicate semimetals,” they generically …

A relativistic helicity has been formulated in the four-dimensional Minkowski space-time.
Whereas the relativistic distortion of space-time violates the conservation of the conventional …

We examine a stochastic Landau–Lifshitz–Gilbert equation based on an exchange energy
functional containing second-order derivatives of the unknown field. Such regularizations …

The linking number is usually defined as an isotopy invariant of two non-intersecting closed
curves in 3-dimensional space. However, the original definition in 1833 by Gauss in the form …

If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws
arise. For a class of zero-helicity vorticity fields, the Godbillon-Vey (GV) invariant of foliations …

We construct two-band topological semimetals in four dimensions using the unstable
homotopy of maps from the three-torus $ T^ 3$(Brillouin zone of a 3D crystal) to the two …

Liquid crystals are materials with interesting symmetries and order, and their science and
applications are a playground of geometry and elasticity. I discuss various aspects of the …

Let m and be positive integers. The set of links of codimension,, is the set of smooth isotopy
classes of smooth embeddings. Haefliger showed that is a finitely generated abelian group …

The based loop space of a configuration space of points in a Euclidean space can be
viewed as a space of pure braids in a Euclidean space of one dimension higher. We …