Nonabelian Tensor Squares of Compact Groups via Quotients of Free Compact Groups

We provide an explicit construction for the nonabelian tensor square of compact groups in terms of quotients of free compact groups. This has several consequences in terms of structural results and, just to mention two of them, one is a new upper bound for the weight of the nonabelian tensor square, another is the description of complements for the nonabelian tensor squares when we focus on the case of pro-p-groups.