Title: Topological Interplay between Knots and Entangled Vortex-Membranes,
Abstract: In this paper, the Kelvin wave and knot dynamics are studied on three
dimensional smoothly deformed entangled vortex-membranes in five dimensional
space. Owing to the existence of local Lorentz invariance and diffeomorphism
invariance, in continuum limit gravity becomes an emergent phenomenon on 3+1
dimensional zero-lattice (a lattice of projected zeroes): On the one hand, the
deformed zero-lattice can be denoted by curved space-time for knots; on the
other hand, the knots as topological defect of 3+1 dimensional zero-lattice
indicates matter may curve space-time. This work would help researchers to
understand the mystery in gravity.