Topological Aspects in an Interacting Mixture of a Charged and a Neutral Superfluid in Neutron Stars

By making use of the decomposition of U（1） gauge potential theory and the C-mapping method we discuss a mixture of interacting neutral and charged Bose condensates, which is supposed to be realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonie superconductor. We propose that this system possesses vortex line knotted solitons and the topological charges of vortex lines are characterized by the winding numbers of the C-mapping. Furthermore the spatial bifurcation of vortices is also discussed.     

Topological structure of Gauss-Bonnet-Chern theorem and -branes

By making use of the φ-mapping topological current theory, this paper shows that the Gauss-Bonnet-Chern density (the Euler-Poincaré characteristic χ(M) density) can be expressed in terms of a smooth vector field φ and take the form of δ(φ), which means that only the zeros of φ contribute to χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes.