# Spin-statistics theorem on spaces with non-integer dimensions

What would be the spin-statistics relation for particles 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!