  We classify vortex-core structures according to the topology of the order
parameter space. By developing a method to characterize how the order parameter
changes inside the vortex core. We apply this method to the spin-1
Bose-Einstein condensates and show that the vortex-core structures are
classified by winding numbers that are locally defined in the core region. We
also show that a vortex-core structure with a nontrivial winding number can be
stabilized under a negative quadratic Zeeman effect.

Quantum Gases;High Energy Physics - Phenomenology;High Energy Physics - Theory