I heard that anyons can only be made in 2 dimensions because when you visualize the spacetime diagram of a 2-dimensional system with point particles, you can get braids, but if you do the same with a 3-dimensional system, you get only the un-braid since all braids can be unbraided in 4 dimensions.

But we can make braided surfaces in 4-dimensions by moving around rings in 3 dimensions! So does that mean we get 3 dimensional anyons if there are rings that behave like point-particle anyons?

I tried googling the keywords, but got no answers. I did find a video talking about braided surfaces using rings (Braids in Higher Dimensions - Numberphile).

I heard that anyons can only be made in 2 dimensions because when you visualize the spacetime diagram of a 2-dimensional system with point particles, you can get braids, but if you do the same with a 3-dimensional system, you get only the un-braid since all braids can be unbraided in 4 dimensions.

But we can make braided surfaces in 4-dimensions by moving around rings in 3 dimensions! So does that mean we get 3 dimensional anyons if there are rings that behave like point-particle anyons?

I tried googling the keywords, but got no answers. I did find a video talking about braided surfaces using rings.