More complicated Hilbert spaces can be constructed corresponding to the fusion of three or more particles, i.e. for the quantum systems where it is known that the a 1 , a 2 , … … a m fuse into final anyon type c . This Hilbert space V a 1 , a 2 , … … a m c would describe, for example, the quantum system formed by starting with a quasiparticle c and, via some local physical procedure, splitting up that quasiparticle into quasiparticles a 1 , a 2 , … … a m (because in such a system all the anyons must necessarily fuse back into c by topological invariance). There is an isomorphism between V a 1 , a 2 , … … a m 1 and V a j + 1 , a j + 2 , … … a m a ¯ ¯ 1 , a ¯ ¯ 2 , … … a ¯ ¯ j for any j . As mentioned in the previous section, the permutations of the labels are also isomorphic.