We define a subpower Higson corona of a metric space. This corona turns out to be an intermediate corona between the Higson corona and sublinear Higson corona. It is proved that the subpower compactification of an unbounded ...

We prove that the elements of the Hanoi Towers groups Hm have depth bounded from above by a poly-logarithmic function O(logm⁻²n), where n is the length of an element. Therefore the word problem in groups Hm is solvable in ...