For 1-dimensional space, the fundamental group of SO（1）is a single point. It is trivial. This fact is consistent with physics: it is impossible to exchange two particles in a 1-dimensional space.Particles in such spacetime can carry any spins.

For higher dimensional n+1 spacetime, the symmetry groups are SO(n) and their fundamental groups are the same as that of SO(3), i.e.,Z2. Therefore, there are two and only two types of particles in higher dimensional spacetime.

In string theory, the most fundamental 'stuff' is strings; particles are different vibrational modes of strings. However, the types of paticles are the same in ordinary QFT.