Considering that Braid groups are defined over linear 1D lattices, I am pondering what would be the multidimensional equivalent of Braid groups, when we consider endomorphisms between 2D lattices, or higher dimensional lattices
I understand there is some nuance to be had to be precise, as above 3 dimensions, tangles of 1D braids should all collapse to their permutation group restriction, but not clear how to formulate that precisely in general