Divisibility of Spheres with Measurable Pieces

Clinton T. Conley, Jan Grebík, Oleg Pikhurko

For an $r$-tuple $({\gamma }_1,\dots ,{\gamma }_r)$ of special orthogonal $d\times d$ matrices, we say that the Euclidean $(d-1)$-dimensional sphere $S^{d-1}$ is $({\gamma }_1,\dots ,{\gamma }_r)$-divisible if th…