Thed-invariant of compact nilmanifolds
Copyright policy )Thed-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.
- DigiZeitschriften Germany
- University of Cologne Germany
Adams-d-invariant, \(J\)-morphism, Article, 510.mathematics, Stable homotopy of spheres, simply connected nilpotent Lie group, Index theory and related fixed-point theorems on manifolds, index of the Dirac operator, framed manifolds, Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory, stable homotopy groups of spheres
Adams-d-invariant, \(J\)-morphism, Article, 510.mathematics, Stable homotopy of spheres, simply connected nilpotent Lie group, Index theory and related fixed-point theorems on manifolds, index of the Dirac operator, framed manifolds, Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory, stable homotopy groups of spheres
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