What would be the spin-statistics relation for particles (including quasiparticles cf. anyons in 2+1 dimensions) in a space with non-integer dimension, $ 2 \lt D \lt 3 $? In other words (cf. stackexchange questions here and here), what is the first homotopy group for a space with non-integer dimension, $ 2 \lt D \lt 3 $?
Although it is not useful for my immediate work, I would also like to know for fractional dimensions $ 0 \lt D \lt 2 $ and $ 3 \lt D \lt \infty $
References/reviews, written for physicists, will also be greatly appreciated!
This post imported from StackExchange Physics at 2014-08-11 14:13 (UCT), posted by SE-user crackjack