It is shown that flat zero-energy solutions (vacua) of the 5d Kaluza-Klein
theory admit a non-trivial homotopy structure generated by certain Kaluza-Klein
excitations. These vacua consist of an infinite set of homotopically different
spacetimes denoted by M5(n)β, among which M5(0)β
and M5(1)β are especially identified as M4βΓS1 and
M5β, the ground states of the 5d Kaluza-Klein theory and the 5d general
relativity, respectively (where Mkβ represents the k-dimensional Minkowski
space).Comment: 8 page