In topology, a branch of mathematics, a nilpotent space, first defined by Emmanuel Dror, is a based topological space X such that the fundamental group π = π 1 {\displaystyle \pi =\pi _{1}} is a nilpotent group; π {\displaystyle \pi } acts nilpotently on the higher homotopy groups π i, i ≥ 2 {\displaystyle \pi _{i},i\geq 2}, i.e., there is a central series π i = G 1 i ▹ G 2 i ▹ ⋯ ▹ G n i i = 1 {\displaystyle \pi _{i}=G_{1}^{i}\triangleright G_{2}^{i}\triangleright \dots \triangleright G_{n_{i}}^{i}=1} such that the induced action of π {\displaystyle \pi } on the quotient group G k i / G k + 1 i {\displaystyle G_{k}^{i}/G_{k+1}^{i}} is trivial for all k {\displaystyle k}. Wikipedia