The d-invariant of compact nilmanifolds
Let G be a simply connected nilpotent Lie group and \(\Gamma\) a discrete subgroup such that G/\(\Gamma\) is compact. Then a choice of an orientation provides G/\(\Gamma\) with a stable framing. In this note it is shown that the Adams-d-invariant d[G/\(\Gamma\) ] vanishes (if dim G\(>2)\). The proof uses the relation of the d-invariant to the index of the Dirac operator; it proceeds by comparison through a sequence of discrete subgroups \(\Gamma_ i\) of G.
scientific article; zbMATH DE number 3890356