In general, it is possible to link two 
-dimensional hyperspheres in
-dimensional space in an infinite
number of inequivalent ways. In dimensions greater than 
in the piecewise linear category, it is true that these
spheres are themselves unknotted. However, they may still form nontrivial links.
In this way, they are something like higher dimensional analogs of two one-spheres
in three dimensions. The following table gives the number of nontrivial ways that
two 
-dimensional hyperspheres
can be linked in 
dimensions.
| D of spheres | D of space | distinct linkings |
| 23 | 40 | 239 |
| 31 | 48 | 959 |
| 102 | 181 | 3 |
| 102 | 182 | 10438319 |
| 102 | 183 | 3 |
Two 10-dimensional hyperspheres link up in 12, 13, 14, 15, and 16 dimensions, unlink in 17 dimensions, then link up again in 18, 19, 20, and 21 dimensions. The proof of these results consists of an "easy part" (Zeeman 1962) and "hard part" (Ravenel 1986). The hard part is related to the calculation of the (stable and unstable) homotopy groups of spheres.
