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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!

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